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Combinatorial Methods in Topology and Algebraic Geometry

Combinatorial Methods in Topology and Algebraic Geometry Author John R. Harper
ISBN-10 0821850393
Release 1985
Pages 349
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This collection marks the recent resurgence of interest in combinatorial methods, resulting from their deep and diverse applications both in topology and algebraic geometry. Nearly thirty mathematicians met at the University of Rochester in 1982 to survey several of the areas where combinatorial methods are proving especially fruitful: topology and combinatorial group theory, knot theory, 3-manifolds, homotopy theory and infinite dimensional topology, and four manifolds and algebraic surfaces. This material is accessible to advanced graduate students with a general course in algebraic topology along with some work in combinatorial group theory and geometric topology, as well as to established mathematicians with interests in these areas.For both student and professional mathematicians, the book provides practical suggestions for research directions still to be explored, as well as the aesthetic pleasures of seeing the interplay between algebra and topology which is characteristic of this field. In several areas the book contains the first general exposition published on the subject. In topology, for example, the editors have included M. Cohen, W. Metzler and K. Sauerman's article on 'Collapses of $K\times I$ and group presentations' and Metzler's 'On the Andrews-Curtis-Conjecture and related problems'. In addition, J. M. Montesino has provided summary articles on both 3 and 4-manifolds.

Categorification in Geometry Topology and Physics

Categorification in Geometry  Topology  and Physics Author Anna Beliakova
ISBN-10 9781470428211
Release 2017-02-21
Pages 267
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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

Differential Geometry and Topology Author A.T. Fomenko
ISBN-10 9780306109959
Release 1987-05-31
Pages 344
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Differential Geometry and Topology has been writing in one form or another for most of life. You can find so many inspiration from Differential Geometry and Topology also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Differential Geometry and Topology book for free.

Geometry and Topology Down Under

Geometry and Topology Down Under Author Craig D. Hodgson
ISBN-10 9780821884805
Release 2013-08-23
Pages 369
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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.

Compact Riemann Surfaces

Compact Riemann Surfaces Author Jürgen Jost
ISBN-10 9783662034460
Release 2013-04-17
Pages 295
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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.

Symplectic Geometry

Symplectic Geometry Author A.T. Fomenko
ISBN-10 2881249019
Release 1995-11-30
Pages 484
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Symplectic Geometry has been writing in one form or another for most of life. You can find so many inspiration from Symplectic Geometry also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Symplectic Geometry book for free.

Bridging Algebra Geometry and Topology

Bridging Algebra  Geometry  and Topology Author Denis Ibadula
ISBN-10 9783319091860
Release 2014-10-20
Pages 289
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Algebra, geometry and topology cover a variety of different, but intimately related research fields in modern mathematics. This book focuses on specific aspects of this interaction. The present volume contains refereed papers which were presented at the International Conference “Experimental and Theoretical Methods in Algebra, Geometry and Topology”, held in Eforie Nord (near Constanta), Romania, during 20-25 June 2013. The conference was devoted to the 60th anniversary of the distinguished Romanian mathematicians Alexandru Dimca and Ştefan Papadima. The selected papers consist of original research work and a survey paper. They are intended for a large audience, including researchers and graduate students interested in algebraic geometry, combinatorics, topology, hyperplane arrangements and commutative algebra. The papers are written by well-known experts from different fields of mathematics, affiliated to universities from all over the word, they cover a broad range of topics and explore the research frontiers of a wide variety of contemporary problems of modern mathematics.

Topology of Algebraic Varieties and Singularities

Topology of Algebraic Varieties and Singularities Author Anatoly Libgober
ISBN-10 9780821848906
Release 2011
Pages 467
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This volume contains invited expository and research papers from the conference Topology of Algebraic Varieties, in honor of Anatoly Libgober's 60th birthday, held June 22-26, 2009, in Jaca, Spain. The volume contains four parts corresponding to the four main focal points of the conference: algebraic geometry and fundamental groups, braids and knots, hyperplane arrangements, and singularities. Together, the papers provide an overview of the current status of a broad range of topological questions in Algebraic Geometry.

Topological and Algebraic Geometry Methods in Contemporary Mathematical Physics

Topological and Algebraic Geometry Methods in Contemporary Mathematical Physics Author B. A. Dubrovin
ISBN-10 1904868304
Release 2004-01
Pages 139
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This volume is a classic survey of algebraic geometry and topological methods in various problems of mathematical physics and provides an excellent reference text for graduate students and researchers. The book is divided into three parts: the first part concerns Hamiltonian formalism and methods that generalise Morse for certain dynamical systems of physical origin; the second part presents algebraic geometry analysis of the Yang-Baxter equations for two-dimensional models; and finally, part three presents the theory of multidimensional theta functions of Abel, Riemann, Poincare in a form that is elementally and convenient for applications.

Geometric Topology Recent Developments

Geometric Topology  Recent Developments Author Jeff Cheeger
ISBN-10 9783540466512
Release 2006-11-17
Pages 200
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Geometric Topology Recent Developments has been writing in one form or another for most of life. You can find so many inspiration from Geometric Topology Recent Developments also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Geometric Topology Recent Developments book for free.

Laminations and Foliations in Dynamics Geometry and Topology

Laminations and Foliations in Dynamics  Geometry and Topology Author Mikhail Lyubich
ISBN-10 9780821819852
Release 2001
Pages 233
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This volume is based on a conference held at SUNY, Stony Brook (NY). The concepts of laminations and foliations appear in a diverse number of fields, such as topology, geometry, analytic differential equations, holomorphic dynamics, and renormalization theory. Although these areas have developed deep relations, each has developed distinct research fields with little interaction among practitioners. The conference brought together the diverse points of view of researchers from different areas. This book includes surveys and research papers reflecting the broad spectrum of themes presented at the event. Of particular interest are the articles by F. Bonahon, ``Geodesic Laminations on Surfaces'', and D. Gabai, ``Three Lectures on Foliations and Laminations on 3-manifolds'', which are based on minicourses that took place during the conference.

Topology and Geometry in Dimension Three

Topology and Geometry in Dimension Three Author William H. Jaco
ISBN-10 9780821852958
Release 2011
Pages 196
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This volume contains the proceedings of a conference held from June 4-6, 2010, at Oklahoma State University, in honor of William (Bus) Jaco's 70th birthday. His contributions to research in low dimensional geometry and topology and to the American mathematical community, especially through his work for the American Mathematical Society, were recognized during the conference. The focus of the conference was on triangulations and geometric structures for three-dimensional manifolds. The papers in this volume present significant new results on these topics, as well as in geometric group theory.

Geometric and Topological Methods for Quantum Field Theory

Geometric and Topological Methods for Quantum Field Theory Author Sylvie Paycha
ISBN-10 9780821840627
Release 2007
Pages 255
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This volume, based on lectures and short communications at a summer school in Villa de Leyva, Colombia (July 2005), offers an introduction to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. It is aimed at graduate students in physics or mathematics who might want insight in the following topics (covered in five survey lectures): Anomalies and noncommutative geometry, Deformation quantisation and Poisson algebras, Topological quantum field theory and orbifolds. These lectures are followed by nine articles on various topics at the borderline of mathematics and physics ranging from quasicrystals to invariant instantons through black holes, and involving a number of mathematical tools borrowed from geometry, algebra and analysis.

Elements of Point Set Topology

Elements of Point Set Topology Author John D. Baum
ISBN-10 9780486668260
Release 1964
Pages 150
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Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.

Geometry Topology and Mathematical Physics

Geometry  Topology  and Mathematical Physics Author V. M. Buchstaber
ISBN-10 0821836137
Release 2004
Pages 324
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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.

Surveys in Contemporary Mathematics

Surveys in Contemporary Mathematics Author Nicholas Young
ISBN-10 9780521705646
Release 2008
Pages 361
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A collection of articles showcasing the achievements of young Russian researchers in combinatorial and algebraic geometry and topology.

Geometry and Physics

Geometry and Physics Author Jürgen Jost
ISBN-10 3642005411
Release 2009-08-17
Pages 217
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"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.