geometric topology contemporary mathematics

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Categorification In Geometry Topology And Physics

Author : Anna Beliakova
ISBN : 9781470428211
Genre : Categories (Mathematics)
File Size : 33. 23 MB
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The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorification is a powerful tool for relating various branches of mathematics and exploiting the commonalities between fields. It provides a language emphasizing essential features and allowing precise relationships between vastly different fields. This volume focuses on the role categorification plays in geometry, topology, and physics. These articles illustrate many important trends for the field including geometric representation theory, homotopical methods in link homology, interactions between higher representation theory and gauge theory, and double affine Hecke algebra approaches to link homology. The companion volume (Contemporary Mathematics, Volume 683) is devoted to categorification and higher representation theory.

Differential Geometry And Topology

Author : A.T. Fomenko
ISBN : 9780306109959
Genre : Mathematics
File Size : 70. 50 MB
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Compact Riemann Surfaces

Author : Jürgen Jost
ISBN : 9783662034460
Genre : Mathematics
File Size : 32. 58 MB
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This book is novel in its broad perspective on Riemann surfaces: the text systematically explores the connection with other fields of mathematics. The book can serve as an introduction to contemporary mathematics as a whole, as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. The book is unique among textbooks on Riemann surfaces in its inclusion of an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.

Geometric Topology Recent Developments

Author : Jeff Cheeger
ISBN : 9783540466512
Genre : Mathematics
File Size : 67. 88 MB
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Algebraic And Geometric Combinatorics

Author : Christos A. Athanasiadis
ISBN : 9780821840801
Genre : Mathematics
File Size : 40. 53 MB
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This volume contains original research and survey articles stemming from the Euroconference ""Algebraic and Geometric Combinatorics"". The papers discuss a wide range of problems that illustrate interactions of combinatorics with other branches of mathematics, such as commutative algebra, algebraic geometry, convex and discrete geometry, enumerative geometry, and topology of complexes and partially ordered sets. Among the topics covered are combinatorics of polytopes, lattice polytopes, triangulations and subdivisions, Cohen-Macaulay cell complexes, monomial ideals, geometry of toric surfaces, groupoids in combinatorics, Kazhdan-Lusztig combinatorics, and graph colorings. This book is aimed at researchers and graduate students interested in various aspects of modern combinatorial theories.

Geometry Topology And Mathematical Physics

Author : V. M. Buchstaber
ISBN : 0821836137
Genre : Mathematics
File Size : 74. 94 MB
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This volume contains a selection of papers based on presentations given at the S. P. Novikov seminar held at the Steklov Mathematical Institute in Moscow. Topics and speakers were chosen by the well-known expert, S. P. Novikov, one of the leading mathematicians of the twentieth century. His diverse interests are the tradition of the seminar and are reflected in the topics presented in the book. The book begins with Novikov's paper analyzing the position of mathematics and theoretical physics at the beginning of the new millennium. Following is an interview with Novikov published in the Newsletter of the European Mathematical Society presenting the genesis of many of his ideas and his scientific school. The remaining articles address topics in geometry, topology, and mathematical physics. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.

Geometry And Topology Down Under

Author : Craig D. Hodgson
ISBN : 9780821884805
Genre : Mathematics
File Size : 64. 93 MB
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This book contains the proceedings of the conference Geometry & Topology Down Under, held July 11-22, 2011, at the University of Melbourne, Parkville, Australia, in honour of Hyam Rubinstein. The main topic of the book is low-dimensional geometry and topology. It includes both survey articles based on courses presented at the conferences and research articles devoted to important questions in low-dimensional geometry. Together, these contributions show how methods from different fields of mathematics contribute to the study of 3-manifolds and Gromov hyperbolic groups. It also contains a list of favorite problems by Hyam Rubinstein.

The Influence Of Solomon Lefschetz In Geometry And Topology

Author : Ernesto Lupercio
ISBN : 9780821894941
Genre : Mathematics
File Size : 22. 74 MB
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The influence of Solomon Lefschetz (1884-1972) in geometry and topology 40 years after his death has been very profound. Lefschetz's influence in Mexican mathematics has been even greater. In this volume, celebrating 50 years of mathematics at Cinvestav-México, many of the fields of geometry and topology are represented by some of the leaders of their respective fields. This volume opens with Michael Atiyah reminiscing about his encounters with Lefschetz and México. Topics covered in this volume include symplectic flexibility, Chern-Simons theory and the theory of classical theta functions, toric topology, the Beilinson conjecture for finite-dimensional associative algebras, partial monoids and Dold-Thom functors, the weak b-principle, orbit configuration spaces, equivariant extensions of differential forms for noncompact Lie groups, dynamical systems and categories, and the Nahm pole boundary condition.

Surveys In Contemporary Mathematics

Author : Nicholas Young
ISBN : 9780521705646
Genre : Mathematics
File Size : 46. 23 MB
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A collection of articles showcasing the achievements of young Russian researchers in combinatorial and algebraic geometry and topology.

Symplectic Geometry

Author : A.T. Fomenko
ISBN : 2881249019
Genre : Mathematics
File Size : 33. 99 MB
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