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Introduction to Topological Manifolds

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Springer, 1 janv. 2000 - 385 pages
This book is an introduction to manifolds at the beginning graduate level. 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. Its guiding philosophy is to develop these ideas rigorously but economically, with minimal prerequisites and plenty of geometric intuition. A course on manifolds differs from most other introductory mathematics graduate courses in that the subject matter is often completely unfamiliar. Unlike algebra and analysis, which all math majors see as undergraduates, manifolds enter the curriculum much later. It is even possible to get through an entire undergraduate mathematics education without ever hearing the word "manifold." Yet manifolds are part of the basic vocabulary of modern mathematics, and students need to know them as intimately as they know the integers, the real numbers, Euclidean spaces, groups, rings, and fields. In his beautifully-conceived Introduction, the author motivates the technical developments to follow by explaining some of the roles manifolds play in diverse branches of mathematics and physics. Then he goes on to introduce the basics of general topology and continues with the fundamental group, covering spaces, and elementary homology theory. Manifolds are introduced early and used as the main examples throughout. John M. Lee is currently Professor of Mathematics at the University of Washington in Seattle. In addition to pursuing research in differential geometry and partial differential equations, he has been teaching undergraduate and graduate courses on manifolds at U.W. and Harvard University for more than fifteen years.
  

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Review: Introduction to Topological Manifolds

Avis d'utilisateur  - Joecolelife - Goodreads

I began learning topology beyond real analysis with this book, and I found it to be a well-balanced text. This book covers every fundamental subject one needs to know without delving too much into a ... Consulter l'avis complet

Review: Introduction to Topological Manifolds

Avis d'utilisateur  - Joecolelife - Goodreads

The only other books I have seen that deserve the title of both a reference and a textbook are by Lang. That being said, the exposition is at the other end of the spectrum with the goal being to teach ... Consulter l'avis complet

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Table des matières

Introduction I
1
Topological Spaces
17
New Spaces from Old
39
Connectedness and Compactness
65
Simplicial Complexes 01
91
Curves and Surfaces
117
Homotopy and the Fundamental Group
147
Circles and Spheres
179
The SeifertVan Kampen Theorem
209
Covering Spaces
233
Classification of Coverings
257
Homology
292
Review of Prerequisites
337
Metric Spaces
347
References
359
Droits d'auteur

g Some Group Theory 103
194

Autres éditions - Tout afficher

Introduction to Topological Manifolds
Introduction to Topological Manifolds
John M. Lee
Aperçu limité - 2000
Introduction to topological manifolds
Introduction to topological manifolds

Aperçu limité - 2000
Introduction to Topological Manifolds
Introduction to Topological Manifolds
John M. Lee
Aperçu limité - 2000
Tout afficher »

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JSTOR: Introduction to Topological Manifolds
Introduction to topological manifolds, by John M. Lee. Graduate Texts in Mathematics 202. Pp.385. ?48 (hb), ?24 (pb). 2000. ISBN 0 387 98759 2 (hb), ...
links.jstor.org/ sici?sici=0025-5572(200103)2%3A85%3A502%3C183%3AITTM%3E2.0.CO%3B2-J

Corrections to Introduction to Topological Manifolds, Draft Second ...
Introduction to Topological Manifolds, Draft Second Edition. by John M. Lee. December 7, 2006. (10/2/06) Page 7, second-to-last paragraph, ...
www.math.washington.edu/ ~lee/ Courses/ 544-2006/ errata.pdf

Introduction to Topological Manifolds - Manifolds and Cell ...
Introduction to Topological Manifolds - Geometry & Topology. This book is an introduction to manifolds at the beginning graduate level.
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Corrections to Introduction to Topological Manifolds
Introduction to Topological Manifolds. by John M. Lee. October 17, 2007. Changes or additions made in the past twelve months are dated. ...
www.math.washington.edu/ ~lee/ Books/ Manifolds/ errata.pdf

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Informations bibliographiques

QR code for Introduction to Topological Manifolds
TitreIntroduction to Topological Manifolds
Volume 202 de Graduate Texts in Mathematics, ISSN 0072-5285
AuteurJohn M. Lee
Éditionillustrée
ÉditeurSpringer, 2000
ISBN0387950265, 9780387950266
Longueur385 pages
  
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