Russian Mathematical Topology Filetype Pdf
"This book is about toric topology, a new area of mathematics that emerged at the end of the 1990s on the border of equivariant topology, algebraic and symplectic geometry, combinatorics, and commutative algebra.
Author: V. M. Buchstaber
Publisher:
ISBN: 147042214X
Category: Algebraic topology
Page: 518
View: 544
"This book is about toric topology, a new area of mathematics that emerged at the end of the 1990s on the border of equivariant topology, algebraic and symplectic geometry, combinatorics, and commutative algebra. It has quickly grown into a very active area with many links to other areas of mathematics, and continues to attract experts from different fields. The key players in toric topology are moment-angle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of moment-angle manifolds relates to combinatorial geometry and algebraic geometry of toric varieties via the notion of a quasitoric manifold. Discovery of remarkable geometric structures on moment-angle manifolds led to important connections with classical and modern areas of symplectic, Lagrangian, and non-Kaehler complex geometry. A related categorical construction of moment-angle complexes and polyhedral products provides for a universal framework for many fundamental constructions of homotopical topology. The study of polyhedral products is now evolving into a separate subject of homotopy theory. A new perspective on torus actions has also contributed to the development of classical areas of algebraic topology, such as complex cobordism. This book includes many open problems and is addressed to experts interested in new ideas linking all the subjects involved, as well as to graduate students and young researchers ready to enter this beautiful new area"--Back cover.
V.M. Buchstaber, "Toric Topology of Stasheff Polytopes," MIMS EPrint: 2007.232. 7. ... "Algebraic topology of manifolds defined by simple polytopes", Russian Mathematical Surveys, 1998, 53:3, pp. ... Surveys and Monographs, vol.
Author: Darby Alastair
Publisher: World Scientific
ISBN: 9789813226586
Category: Mathematics
Page: 448
View: 114
This volume consists of introductory lectures on the topics in the new and rapidly developing area of toric homotopy theory, and its applications to the current research in configuration spaces and braids, as well as to more applicable mathematics such as fr-codes and robot motion planning. The book starts intertwining homotopy theoretical and combinatorial ideas within the remits of toric topology and illustrates an attempt to classify in a combinatorial way polytopes known as fullerenes, which are important objects in quantum physics, quantum chemistry and nanotechnology. Toric homotopy theory is then introduced as a further development of toric topology, which describes properties of Davis–Januszkiewicz spaces, moment-angle complexes and their generalizations to polyhedral products. The book also displays the current research on configuration spaces, braids, the theory of limits over the category of presentations and the theory of fr-codes. As an application to robotics, the book surveys topological problems relevant to the motion planning problem of robotics and includes new results and constructions, which enrich the emerging area of topological robotics. The book is at research entry level addressing the core components in homotopy theory and their important applications in the sciences and thus suitable for advanced undergraduate and graduate students. Contents: Toric Homotopy Theory (Stephen Theriault)Fullerenes, Polytopes and Toric Topology (Victor M Buchstaber and Nikolay Yu Erokhovets)Around Braids (Vladimir Vershinin)Higher Limits, Homology Theories and fr-Codes (Sergei O Ivanov and Roman Mikhailov)Configuration Spaces and Robot Motion Planning Algorithms (Michael Farber)Cellular Stratified Spaces (Dai Tamaki) Readership: Advanced undergraduate and graduate students as well as researchers interested in homotopy theory and its applications in the sciences. Keywords: Toric Topology;Toric Homotopy;Configuration Space;Stratified Spaces;Braid Group;Fullerene;Polytope;Virtual Braid Group;Thompson Group;Robotics;Motion PlanningReview: Key Features: The first book in the area of toric homotopy theory consisting of introductory lectures on the topics and their applications to fr-codes and robot motion planning
Jörg Gretenkort, Peter Kleinschmidt and Bernd Sturmfels, On the existence of certain smooth toric varieties. ... Moment maps, cobordisms, and Hamiltonian group actions. Mathematical Surveys and Monographs, 98. Amer. Math.
Author: Victor M. Buchstaber
Publisher: American Mathematical Soc.
ISBN: 9781470422141
Category: Algebraic topology
Page: 518
View: 977
This book is about toric topology, a new area of mathematics that emerged at the end of the 1990s on the border of equivariant topology, algebraic and symplectic geometry, combinatorics, and commutative algebra. It has quickly grown into a very active area with many links to other areas of mathematics, and continues to attract experts from different fields. The key players in toric topology are moment-angle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of moment-angle manifolds relates to combinatorial geometry and algebraic geometry of toric varieties via the notion of a quasitoric manifold. Discovery of remarkable geometric structures on moment-angle manifolds led to important connections with classical and modern areas of symplectic, Lagrangian, and non-Kaehler complex geometry. A related categorical construction of moment-angle complexes and polyhedral products provides for a universal framework for many fundamental constructions of homotopical topology. The study of polyhedral products is now evolving into a separate subject of homotopy theory. A new perspective on torus actions has also contributed to the development of classical areas of algebraic topology, such as complex cobordism. This book includes many open problems and is addressed to experts interested in new ideas linking all the subjects involved, as well as to graduate students and young researchers ready to enter this beautiful new area.
V. Buchstaber, T. Panov, Toric Topology, Mathematical surveys and monographs, vol. 204. (American Mathematical Society, Providence, 2015) A. Darby, S. Kuroki, J. Song, Equivariant cohomology of torus orbifolds, arXiv:1809.03678 9.
Author: Mahender Singh
Publisher: Springer
ISBN: 9789811357428
Category: Mathematics
Page: 313
View: 464
This book highlights the latest advances in algebraic topology, from homotopy theory, braid groups, configuration spaces and toric topology, to transformation groups and the adjoining area of knot theory. It consists of well-written original research papers and survey articles by subject experts, most of which were presented at the "7th East Asian Conference on Algebraic Topology" held at the Indian Institute of Science Education and Research (IISER), Mohali, Punjab, India, from December 1 to 6, 2017. Algebraic topology is a broad area of mathematics that has seen enormous developments over the past decade, and as such this book is a valuable resource for graduate students and researchers working in the field.
Series of Discrete Applied Mathematics. Boca Raton, FL: CRC Press, 2004, pp. 420–430. ... [in Russian] Buchstaber V.M., Panov T.E. Toric topology. Mathematical Surveys and Monographs, 204. Providence, RI: American Mathematical Society, ...
Author: Andrey O. Matveev
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 9783110531145
Category: Mathematics
Page: 231
View: 270
Pattern Recognition on Oriented Matroids covers a range of innovative problems in combinatorics, poset and graph theories, optimization, and number theory that constitute a far-reaching extension of the arsenal of committee methods in pattern recognition. The groundwork for the modern committee theory was laid in the mid-1960s, when it was shown that the familiar notion of solution to a feasible system of linear inequalities has ingenious analogues which can serve as collective solutions to infeasible systems. A hierarchy of dialects in the language of mathematics, for instance, open cones in the context of linear inequality systems, regions of hyperplane arrangements, and maximal covectors (or topes) of oriented matroids, provides an excellent opportunity to take a fresh look at the infeasible system of homogeneous strict linear inequalities – the standard working model for the contradictory two-class pattern recognition problem in its geometric setting. The universal language of oriented matroid theory considerably simplifies a structural and enumerative analysis of applied aspects of the infeasibility phenomenon. The present book is devoted to several selected topics in the emerging theory of pattern recognition on oriented matroids: the questions of existence and applicability of matroidal generalizations of committee decision rules and related graph-theoretic constructions to oriented matroids with very weak restrictions on their structural properties; a study (in which, in particular, interesting subsequences of the Farey sequence appear naturally) of the hierarchy of the corresponding tope committees; a description of the three-tope committees that are the most attractive approximation to the notion of solution to an infeasible system of linear constraints; an application of convexity in oriented matroids as well as blocker constructions in combinatorial optimization and in poset theory to enumerative problems on tope committees; an attempt to clarify how elementary changes (one-element reorientations) in an oriented matroid affect the family of its tope committees; a discrete Fourier analysis of the important family of critical tope committees through rank and distance relations in the tope poset and the tope graph; the characterization of a key combinatorial role played by the symmetric cycles in hypercube graphs. Contents Oriented Matroids, the Pattern Recognition Problem, and Tope Committees Boolean Intervals Dehn–Sommerville Type Relations Farey Subsequences Blocking Sets of Set Families, and Absolute Blocking Constructions in Posets Committees of Set Families, and Relative Blocking Constructions in Posets Layers of Tope Committees Three-Tope Committees Halfspaces, Convex Sets, and Tope Committees Tope Committees and Reorientations of Oriented Matroids Topes and Critical Committees Critical Committees and Distance Signals Symmetric Cycles in the Hypercube Graphs
716 G. E. Bredon, Topology and geometry, Graduate Texts in Mathematics, vol. 139, Springer-Verlag, New York, 1997, Corrected third ... 279, 381, 526 V. M. Buchstaber and T. E. Panov, Toric topology, Mathematical Surveys and Monographs, ...
Author: Marcelo Aguiar
Publisher: Cambridge University Press
ISBN: 9781108495806
Category: Mathematics
Page: 824
View: 987
Develops a new theory, parallel to the classical theory of connected Hopf algebras, including a real hyperplane arrangement.
MR131880 [6] Michael Atiyah, Topological quantum field theories, Inst. Hautes Etudes ́ Sci. Publ. Math. ... MR0291159 [21] Victor M. Buchstaber and Taras E. Panov, Toric topology, Mathematical Surveys and Monographs, vol.
Author: Anatoly M. Vershik
Publisher: American Mathematical Soc.
ISBN: 9781470456641
Category: Education
Page: 345
View: 684
Vladimir Abramovich Rokhlin (8/23/1919–12/03/1984) was one of the leading Russian mathematicians of the second part of the twentieth century. His main achievements were in algebraic topology, real algebraic geometry, and ergodic theory. The volume contains the proceedings of the Conference on Topology, Geometry, and Dynamics: V. A. Rokhlin-100, held from August 19–23, 2019, at The Euler International Mathematics Institute and the Steklov Institute of Mathematics, St. Petersburg, Russia. The articles deal with topology of manifolds, theory of cobordisms, knot theory, geometry of real algebraic manifolds and dynamical systems and related topics. The book also contains Rokhlin's biography supplemented with copies of actual very interesting documents.
Mirror Symmetry and Algebraic Geometry, Mathematical Surveys and Monographs. Volume 68. [13] W.Fulton. Introduction to Toric Varieyies. Annals of Mathematics Studies. 131. The William H. Roever Lectures in Geometry. Princeton Univ.
Author: Ched E. Stedman
Publisher: Nova Publishers
ISBN: 1600211879
Category: Mathematics
Page: 159
View: 949
This volume gathers results in pure and applied algebra including algebraic topology from researchers around the globe. The selection of these papers was carried out under the auspices of a special editorial board.
K. Costello, Renormalization and effective field theory, Mathematical Surveys and Monographs, vol. ... of open Gromov-Witten invariants for toric CalabiYau 3-folds by topological recursion, a proof of the BKMP conjecture, Comm. Math.
Author: Vincent Bouchard:
Publisher: American Mathematical Soc.
ISBN: 9781470419929
Category: $K$-theory
Page: 396
View: 749
The conference String-Math 2014 was held from June 9–13, 2014, at the University of Alberta. This edition of String-Math is the first to include satellite workshops: "String-Math Summer School" (held from June 2–6, 2014, at the University of British Columbia), "Calabi-Yau Manifolds and their Moduli" (held from June 14–18, 2014, at the University of Alberta), and "Quantum Curves and Quantum Knot Invariants" (held from June 16–20, 2014, at the Banff International Research Station). This volume presents the proceedings of the conference and satellite workshops. For mathematics, string theory has been a source of many significant inspirations, ranging from Seiberg-Witten theory in four-manifolds, to enumerative geometry and Gromov-Witten theory in algebraic geometry, to work on the Jones polynomial in knot theory, to recent progress in the geometric Langlands program and the development of derived algebraic geometry and n-category theory. In the other direction, mathematics has provided physicists with powerful tools, ranging from powerful differential geometric techniques for solving or analyzing key partial differential equations, to toric geometry, to K-theory and derived categories in D-branes, to the analysis of Calabi-Yau manifolds and string compactifications, to modular forms and other arithmetic techniques. Articles in this book address many of these topics.
2013] T. Coates, A. Corti, H. Iritani, and H. H. Tseng, "A mirror theorem for toric stacks", 2013. arXiv 1310.4163 [Cox and Katz 1999] D. A. Cox and S. Katz, Mirror symmetry and algebraic geometry, Mathematical Surveys and Monographs 68 ...
Author: Tohru Eguchi
Publisher: Cambridge University Press
ISBN: 9781107056411
Category: Mathematics
Page: 344
View: 854
Symplectic geometry originated in physics, but it has flourished as an independent subject in mathematics, together with its offspring, symplectic topology. Symplectic methods have even been applied back to mathematical physics. Noncommutative geometry has developed an alternative mathematical quantization scheme based on a geometric approach to operator algebras. Deformation quantization, a blend of symplectic methods and noncommutative geometry, approaches quantum mechanics from a more algebraic viewpoint, as it addresses quantization as a deformation of Poisson structures. This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute: Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology (honoring Alan Weinstein, one of the key figures in the field) and Symplectic Geometry, Noncommutative Geometry and Physics. The chapters include presentations of previously unpublished results and comprehensive reviews, including recent developments in these areas.
... Mathematical Surveys and Monographs, vol. 68, American Mathematical Society, Providence, RI, 1999. MR MR1677117 (2000d:14048) Charles F. Doran and John W. Morgan, Algebraic topology of Calabi-Yau threefolds in toric varieties, Geom.
Author: Ricardo Castaño-Bernard
Publisher: American Mathematical Soc.
ISBN: 9780821848845
Category: Science
Page: 168
View: 747
This volume contains contributions from the NSF-CBMS Conference on Tropical Geometry and Mirror Symmetry, which was held from December 13-17, 2008 at Kansas State University in Manhattan, Kansas. It gives an excellent picture of numerous connections of mirror symmetry with other areas of mathematics (especially with algebraic and symplectic geometry) as well as with other areas of mathematical physics. The techniques and methods used by the authors of the volume are at the frontier of this very active area of research.|This volume contains contributions from the NSF-CBMS Conference on Tropical Geometry and Mirror Symmetry, which was held from December 13-17, 2008 at Kansas State University in Manhattan, Kansas. It gives an excellent picture of numerous connections of mirror symmetry with other areas of mathematics (especially with algebraic and symplectic geometry) as well as with other areas of mathematical physics. The techniques and methods used by the authors of the volume are at the frontier of this very active area of research.
International Mathematics Research Surveys, IMRS 2007, Art. ID rym001, 220pp M. Markl, S. Steve, J. Stasheff, Operads in Algebra, Topology and Physics. Mathematical Surveys and Monographs 96 (American Mathematical Society, Providence, ...
Author: Kenji Fukaya
Publisher: Springer Nature
ISBN: 9789811555626
Category:
Page:
View: 374
[23] D.A.Cox and S. Katz, Mirror symmetry and algebraic geometry, Mathematical Surveys and Monographs, 68 American Mathematical Society, Providence, RI, 1999. [24] V.I. Danilov, The geometry of toric varieties, Russian Math.
Author: Goutam Mukherjee
Publisher: Springer
ISBN: 9789386279309
Category: Mathematics
Page: 140
View: 268
Contributed lectures presented earlier at Winter School on Transformation Groups.
[9] D. A. Cox and S. Katz, Mirror Symmetry and Algebraic Geometry, Math. Surveys and Monographs 68, Amer. Math. ... [22] H. Iritani, Real and integral structures in quantum cohomology I: toric orbifolds, preprint, arXiv:0712.2204.
Author: Hernan Ocampo
Publisher: Cambridge University Press
ISBN: 9781139486736
Category: Science
Page:
View: 258
Aimed at graduate students in physics and mathematics, this book provides an introduction to recent developments in several active topics at the interface between algebra, geometry, topology and quantum field theory. The first part of the book begins with an account of important results in geometric topology. It investigates the differential equation aspects of quantum cohomology, before moving on to noncommutative geometry. This is followed by a further exploration of quantum field theory and gauge theory, describing AdS/CFT correspondence, and the functional renormalization group approach to quantum gravity. The second part covers a wide spectrum of topics on the borderline of mathematics and physics, ranging from orbifolds to quantum indistinguishability and involving a manifold of mathematical tools borrowed from geometry, algebra and analysis. Each chapter presents introductory material before moving on to more advanced results. The chapters are self-contained and can be read independently of the rest.
3, 743 – 766. , Topological invariants of stratified spaces, Springer Monographs in Mathematics, Springer-Verlag ... I Math. 313 (1991), 399–401. V. I. Danilov, The geometry of toric varieties, Russian Math. Surveys 33 (1978), no.
Author: Markus Banagl
Publisher: Springer
ISBN: 9783642125898
Category: Mathematics
Page: 224
View: 455
Intersection cohomology assigns groups which satisfy a generalized form of Poincaré duality over the rationals to a stratified singular space. This monograph introduces a method that assigns to certain classes of stratified spaces cell complexes, called intersection spaces, whose ordinary rational homology satisfies generalized Poincaré duality. The cornerstone of the method is a process of spatial homology truncation, whose functoriality properties are analyzed in detail. The material on truncation is autonomous and may be of independent interest tohomotopy theorists. The cohomology of intersection spaces is not isomorphic to intersection cohomology and possesses algebraic features such as perversity-internal cup-products and cohomology operations that are not generally available for intersection cohomology. A mirror-symmetric interpretation, as well as applications to string theory concerning massless D-branes arising in type IIB theory during a Calabi-Yau conifold transition, are discussed.
Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties. J. Algebraic Geom., 3(3):493–535, ... Mathematical surveys and monographs. American Mathematical Society ... Topology, 35(4):901–929, 1996. Lev Borisov.
Author: Matthew Ballard
Publisher: Springer
ISBN: 9783319916262
Category: Mathematics
Page: 260
View: 576
This book consists of a series of introductory lectures on mirror symmetry and its surrounding topics. These lectures were provided by participants in the PIMS Superschool for Derived Categories and D-branes in July 2016. Together, they form a comprehensive introduction to the field that integrates perspectives from mathematicians and physicists alike. These proceedings provide a pleasant and broad introduction into modern research topics surrounding string theory and mirror symmetry that is approachable to readers new to the subjects. These topics include constructions of various mirror pairs, approaches to mirror symmetry, connections to homological algebra, and physical motivations. Of particular interest is the connection between GLSMs, D-branes, birational geometry, and derived categories, which is explained both from a physical and mathematical perspective. The introductory lectures provided herein highlight many features of this emerging field and give concrete connections between the physics and the math. Mathematical readers will come away with a broader perspective on this field and a bit of physical intuition, while physicists will gain an introductory overview of the developing mathematical realization of physical predictions.
The resulting interaction between algebraic topology, number theory, mathematical physics, and classical geometry will surely prove to be ... Mathematical Surveys and Monographs, 47. ... Fulton W (1993) Introduction to toric varieties.
Author: Nils Baas
Publisher: Springer Science & Business Media
ISBN: 9783642012006
Category: Mathematics
Page: 409
View: 744
The 2007 Abel Symposium took place at the University of Oslo in August 2007. The goal of the symposium was to bring together mathematicians whose research efforts have led to recent advances in algebraic geometry, algebraic K-theory, algebraic topology, and mathematical physics. A common theme of this symposium was the development of new perspectives and new constructions with a categorical flavor. As the lectures at the symposium and the papers of this volume demonstrate, these perspectives and constructions have enabled a broadening of vistas, a synergy between once-differentiated subjects, and solutions to mathematical problems both old and new.
MR3056954 Andrea Brini, Open topological strings and integrable hierarchies: remodeling the Amodel, Comm. Math. Phys. ... David A. Cox and Sheldon Katz, Mirror symmetry and algebraic geometry, Mathematical Surveys and Monographs, vol.
Author: Chiu-Chu Melissa Liu
Publisher: American Mathematical Soc.
ISBN: 9781470435417
Category: Topology
Page: 549
View: 663
This volume contains the proceedings of the 2016 AMS von Neumann Symposium on Topological Recursion and its Influence in Analysis, Geometry, and Topology, which was held from July 4–8, 2016, at the Hilton Charlotte University Place, Charlotte, North Carolina. The papers contained in the volume present a snapshot of rapid and rich developments in the emerging research field known as topological recursion. It has its origin around 2004 in random matrix theory and also in Mirzakhani's work on the volume of moduli spaces of hyperbolic surfaces. Topological recursion has played a fundamental role in connecting seemingly unrelated areas of mathematics such as matrix models, enumeration of Hurwitz numbers and Grothendieck's dessins d'enfants, Gromov-Witten invariants, the A-polynomials and colored polynomial invariants of knots, WKB analysis, and quantization of Hitchin moduli spaces. In addition to establishing these topics, the volume includes survey papers on the most recent key accomplishments: discovery of the unexpected relation to semi-simple cohomological field theories and a solution to the remodeling conjecture. It also provides a glimpse into the future research direction; for example, connections with the Airy structures, modular functors, Hurwitz-Frobenius manifolds, and ELSV-type formulas.
H. Clemens & P. Griffiths, The intermediate Jacobian of the cubic threefold, Ann. Math. (2) 95 (1972), pp. 281–356. 13. D. Cox & S. Katz, Mirror symmetry and algebraic geometry, Mathematical Surveys and Monographs, vol.
Author: Krzysztof Galicki
Publisher: Springer Science & Business Media
ISBN: 9780817647438
Category: Mathematics
Page: 290
View: 169
Riemannian Topology and Structures on Manifolds results from a similarly entitled conference held on the occasion of Charles P. Boyer's 65th birthday. The various contributions to this volume discuss recent advances in the areas of positive sectional curvature, Kähler and Sasakian geometry, and their interrelation to mathematical physics, especially M and superstring theory. Focusing on these fundamental ideas, this collection presents review articles, original results, and open problems of interest.
Math. Phys., 181 (1996), 205–226. [160] L. Le Bruyn, Quotient singularities and the conifold algebra, lecture notes, ... Operads in algebra, topology and physics, volume 96 of Mathematical surveys and monographs, American Mathematical ...
Author: Gwyn Bellamy
Publisher: Cambridge University Press
ISBN: 9781107129542
Category: Mathematics
Page:
View: 416
This book provides a comprehensive introduction to the interactions between noncommutative algebra and classical algebraic geometry.
Russian Mathematical Topology Filetype Pdf
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