Geometry And Topology Of Manifolds Surfaces And Beyond

Author : Vicente Muñoz,Ángel González-Prieto,Juan Ángel Rojo
Publisher : American Mathematical Soc.
Page : 408 pages
File Size : 40,5 Mb
Release : 2020-10-21
Category : Education
ISBN : 9781470461324

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Geometry and Topology of Manifolds: Surfaces and Beyond by Vicente Muñoz,Ángel González-Prieto,Juan Ángel Rojo Pdf

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.

Author : Michael H. Freedman,Frank Quinn
Publisher : Princeton University Press
Page : 268 pages
File Size : 49,5 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781400861064

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Topology of 4-Manifolds (PMS-39), Volume 39 by Michael H. Freedman,Frank Quinn Pdf

One of the great achievements of contemporary mathematics is the new understanding of four dimensions. Michael Freedman and Frank Quinn have been the principals in the geometric and topological development of this subject, proving the Poincar and Annulus conjectures respectively. Recognition for this work includes the award of the Fields Medal of the International Congress of Mathematicians to Freedman in 1986. In Topology of 4-Manifolds these authors have collaborated to give a complete and accessible account of the current state of knowledge in this field. The basic material has been considerably simplified from the original publications, and should be accessible to most graduate students. The advanced material goes well beyond the literature; nearly one-third of the book is new. This work is indispensable for any topologist whose work includes four dimensions. It is a valuable reference for geometers and physicists who need an awareness of the topological side of the field. Originally published in 1990. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : Martin A. Mccrory
Publisher : CRC Press
Page : 370 pages
File Size : 45,6 Mb
Release : 2020-12-18
Category : Mathematics
ISBN : 9781000153934

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Geometry and Topology by Martin A. Mccrory Pdf

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.

Author : Robert Friedman,John W. Morgan
Publisher : Springer Science & Business Media
Page : 532 pages
File Size : 52,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662030288

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Smooth Four-Manifolds and Complex Surfaces by Robert Friedman,John W. Morgan Pdf

In 1961 Smale established the generalized Poincare Conjecture in dimensions greater than or equal to 5 [129] and proceeded to prove the h-cobordism theorem [130]. This result inaugurated a major effort to classify all possible smooth and topological structures on manifolds of dimension at least 5. By the mid 1970's the main outlines of this theory were complete, and explicit answers (especially concerning simply connected manifolds) as well as general qualitative results had been obtained. As an example of such a qualitative result, a closed, simply connected manifold of dimension 2: 5 is determined up to finitely many diffeomorphism possibilities by its homotopy type and its Pontrjagin classes. There are similar results for self-diffeomorphisms, which, at least in the simply connected case, say that the group of self-diffeomorphisms of a closed manifold M of dimension at least 5 is commensurate with an arithmetic subgroup of the linear algebraic group of all automorphisms of its so-called rational minimal model which preserve the Pontrjagin classes [131]. Once the high dimensional theory was in good shape, attention shifted to the remaining, and seemingly exceptional, dimensions 3 and 4. The theory behind the results for manifolds of dimension at least 5 does not carryover to manifolds of these low dimensions, essentially because there is no longer enough room to maneuver. Thus new ideas are necessary to study manifolds of these "low" dimensions.

Author : Stephan C. Carlson
Publisher : John Wiley & Sons
Page : 178 pages
File Size : 54,6 Mb
Release : 2001-01-10
Category : Mathematics
ISBN : UOM:39015049686283

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Topology of Surfaces, Knots, and Manifolds by Stephan C. Carlson Pdf

This textbook contains ideas and problems involving curves, surfaces, and knots, which make up the core of topology. Carlson (mathematics, Rose-Hulman Institute of Technology) introduces some basic ideas and problems concerning manifolds, especially one- and two- dimensional manifolds. A sampling of topics includes classification of compact surfaces, putting more structure on the surfaces, graphs and topology, and knot theory. It is assumed that the reader has a background in calculus. Annotation copyrighted by Book News Inc., Portland, OR.

Author : Stephen Lovett
Publisher : CRC Press
Page : 430 pages
File Size : 40,5 Mb
Release : 2010-06-11
Category : Mathematics
ISBN : 9781439865460

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Differential Geometry of Manifolds by Stephen Lovett Pdf

From the coauthor of Differential Geometry of Curves and Surfaces, this companion book presents the extension of differential geometry from curves and surfaces to manifolds in general. It provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together the classical and modern formulations. The three appendices

Author : Loring W. Tu
Publisher : Springer Science & Business Media
Page : 410 pages
File Size : 53,9 Mb
Release : 2010-10-05
Category : Mathematics
ISBN : 1441974008

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An Introduction to Manifolds by Loring W. Tu Pdf

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'.

Author : Li Chen
Publisher : Unknown
Page : 162 pages
File Size : 47,8 Mb
Release : 2004
Category : Geometry
ISBN : 0975512218

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Discrete Surfaces and Manifolds by Li Chen Pdf

Author : Jennifer Schultens
Publisher : American Mathematical Soc.
Page : 298 pages
File Size : 45,9 Mb
Release : 2014-05-21
Category : Mathematics
ISBN : 9781470410209

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Introduction to 3-Manifolds by Jennifer Schultens Pdf

This book grew out of a graduate course on 3-manifolds and is intended for a mathematically experienced audience that is new to low-dimensional topology. The exposition begins with the definition of a manifold, explores possible additional structures on manifolds, discusses the classification of surfaces, introduces key foundational results for 3-manifolds, and provides an overview of knot theory. It then continues with more specialized topics by briefly considering triangulations of 3-manifolds, normal surface theory, and Heegaard splittings. The book finishes with a discussion of topics relevant to viewing 3-manifolds via the curve complex. With about 250 figures and more than 200 exercises, this book can serve as an excellent overview and starting point for the study of 3-manifolds.

Author : R. James Milgram
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 55,9 Mb
Release : 1978
Category : Mathematics
ISBN : 9780821814338

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Algebraic and Geometric Topology by R. James Milgram Pdf

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.

Author : Danny Calegari
Publisher : Oxford University Press on Demand
Page : 378 pages
File Size : 46,8 Mb
Release : 2007-05-17
Category : Mathematics
ISBN : 9780198570080

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Foliations and the Geometry of 3-Manifolds by Danny Calegari Pdf

This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.

Author : Hans U. Boden
Publisher : American Mathematical Soc.
Page : 368 pages
File Size : 53,7 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 0821871498

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Geometry and Topology of Manifolds by Hans U. Boden Pdf

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 many excellent talks delivered at the conference.

Author : Michael H. Freedman,Feng Luo
Publisher : American Mathematical Soc.
Page : 79 pages
File Size : 52,9 Mb
Release : 1989
Category : Mathematics
ISBN : 9780821870006

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Selected Applications of Geometry to Low-dimensional Topology by Michael H. Freedman,Feng Luo Pdf

The inaugural volume in the popular AMS softcover series designed to make more widely available some of the outstanding lectures presented by various faculty in North America.

Author : John Hempel
Publisher : American Mathematical Society
Page : 209 pages
File Size : 45,5 Mb
Release : 2022-09-21
Category : Mathematics
ISBN : 9781470471644

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3-Manifolds by John Hempel Pdf

A careful and systematic development of the theory of the topology of 3-manifolds, focusing on the critical role of the fundamental group in determining the topological structure of a 3-manifold … self-contained … one can learn the subject from it … would be very appropriate as a text for an advanced graduate course or as a basis for a working seminar. —Mathematical Reviews For many years, John Hempel's book has been a standard text on the topology of 3-manifolds. Even though the field has grown tremendously, the book remains one of the best and most popular introductions to the subject. The theme of this book is the role of the fundamental group in determining the topology of a given 3-manifold. The essential ideas and techniques are covered in the first part of the book: Heegaard splittings, connected sums, the loop and sphere theorems, incompressible surfaces, free groups, and so on. Along the way, many useful and insightful results are proved, usually in full detail. Later chapters address more advanced topics, including Waldhausen's theorem on a class of 3-manifolds that is completely determined by its fundamental group. The book concludes with a list of problems that were unsolved at the time of publication. Hempel's book remains an ideal text to learn about the world of 3-manifolds. The prerequisites are few and are typical of a beginning graduate student. Exercises occur throughout the text.

Author : Jeffrey Marc Lee
Publisher : American Mathematical Soc.
Page : 690 pages
File Size : 42,9 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821848159

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Manifolds and Differential Geometry by Jeffrey Marc Lee Pdf

Differential geometry began as the study of curves and surfaces using the methods of calculus. This book offers a graduate-level introduction to the tools and structures of modern differential geometry. It includes the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, and de Rham cohomology.