Geometry And Topology Of Manifolds
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Geometry And Topology Of Manifolds
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Author : Hans U. Boden
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Geometry And Topology Of Manifolds written by Hans U. Boden and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Manifolds (Mathematics) categories.
This book contains expository papers that give an up-to-date account of recent developments and open problems in the geometry and topology of manifolds, along with several research articles that present new results appearing in published form for the first time. The unifying theme is the problem of understanding manifolds in low dimensions, notably in dimensions three and four, and the techniques include algebraic topology, surgery theory, Donaldson and Seiberg-Witten gauge theory,Heegaard Floer homology, contact and symplectic geometry, and Gromov-Witten invariants. The articles collected for this volume were contributed by participants of the Conference "Geometry and Topology of Manifolds" held at McMaster University on May 14-18, 2004 and are representative of the manyexcellent talks delivered at the conference.
Geometry And Topology Of Manifolds Surfaces And Beyond
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Author : Vicente Muñoz
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-10-21
Geometry And Topology Of Manifolds Surfaces And Beyond written by Vicente Muñoz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-21 with Education categories.
This book represents a novel approach to differential topology. Its main focus is to give a comprehensive introduction to the classification of manifolds, with special attention paid to the case of surfaces, for which the book provides a complete classification from many points of view: topological, smooth, constant curvature, complex, and conformal. Each chapter briefly revisits basic results usually known to graduate students from an alternative perspective, focusing on surfaces. We provide full proofs of some remarkable results that sometimes are missed in basic courses (e.g., the construction of triangulations on surfaces, the classification of surfaces, the Gauss-Bonnet theorem, the degree-genus formula for complex plane curves, the existence of constant curvature metrics on conformal surfaces), and we give hints to questions about higher dimensional manifolds. Many examples and remarks are scattered through the book. Each chapter ends with an exhaustive collection of problems and a list of topics for further study. The book is primarily addressed to graduate students who did take standard introductory courses on algebraic topology, differential and Riemannian geometry, or algebraic geometry, but have not seen their deep interconnections, which permeate a modern approach to geometry and topology of manifolds.
Geometry And Topology
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Author : Martin A. Mccrory
language : en
Publisher: CRC Press
Release Date : 2020-12-18
Geometry And Topology written by Martin A. Mccrory and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-18 with Mathematics categories.
This book discusses topics ranging from traditional areas of topology, such as knot theory and the topology of manifolds, to areas such as differential and algebraic geometry. It also discusses other topics such as three-manifolds, group actions, and algebraic varieties.
Introduction To Topological Manifolds
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Author : John Lee
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-12-25
Introduction To Topological Manifolds written by John Lee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-25 with Mathematics categories.
This book is an introduction to manifolds at the beginning graduate level, and accessible to any student who has completed a solid undergraduate degree in mathematics. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched. The major changes include a new introduction to CW complexes (replacing most of the material on simplicial complexes in Chapter 5); expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps; and a new section on paracompactness.
Geometry Topology And Physics
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Author : Mikio Nakahara
language : en
Publisher: Taylor & Francis
Release Date : 2018-10-03
Geometry Topology And Physics written by Mikio Nakahara and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.
Algebraic And Geometric Topology Part 2
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Author : R. James Milgram
language : en
Publisher: American Mathematical Soc.
Release Date : 1978
Algebraic And Geometric Topology Part 2 written by R. James Milgram and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Mathematics categories.
Contains sections on Structure of topological manifolds, Low dimensional manifolds, Geometry of differential manifolds and algebraic varieties, $H$-spaces, loop spaces and $CW$ complexes, Problems.
Introduction To Topological Manifolds
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Author : John M. Lee
language : en
Publisher: Springer Science & Business Media
Release Date : 2000
Introduction To Topological Manifolds written by John M. Lee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Exercises in the text, especially in the first part of the book. Author states, that they have to be solved, without the solutions, the text is incomplete. Includes also problems after each chapter
The Geometric Topology Of 3 Manifolds
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Author : R. H. Bing
language : en
Publisher: American Mathematical Soc.
Release Date : 1983-12-31
The Geometric Topology Of 3 Manifolds written by R. H. Bing and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-12-31 with Mathematics categories.
Suitable for students and researchers in topology. this work provides the reader with an understanding of the physical properties of Euclidean 3-space - the space in which we presume we live.
An Introduction To Manifolds
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Author : Loring W. Tu
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-05
An Introduction To Manifolds written by Loring W. Tu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-05 with Mathematics categories.
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
Introduction To Topological Manifolds
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Author : John M. Lee
language : en
Publisher:
Release Date : 2011-03-30
Introduction To Topological Manifolds written by John M. Lee and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-30 with categories.