Introduction to Topological Manifolds

Couverture
Springer Science & Business Media, 25 déc. 2010 - 433 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.

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.

This text is designed to be used for an introductory graduate course on the geometry and topology of manifolds. It should be accessible to any student who has completed a solid undergraduate degree in mathematics. The author’s book Introduction to Smooth Manifolds is meant to act as a sequel to this book.

 

Pages sélectionnées

Table des matières

Chapter 1 Introduction
1
Chapter 2 Topological Spaces
18
Chapter 3 New Spaces from Old
49
Chapter 4 Connectedness and Compactness
85
Chapter 5 Cell Complexes
127
Chapter 6 Compact Surfaces
159
Chapter 7 Homotopy and the Fundamental Group
183
Chapter 8 The Circle
217
Chapter 11 Covering Maps
276
Chapter 12 Group Actions and Covering Maps
307
Chapter 13 Homology
338
Review of Set Theory
381
Review of Metric Spaces
395
Review of Group Theory
401
References
407
Notation Index
409

Chapter 9 Some Group Theory
233
Chapter 10 The SeifertVan Kampen Theorem
251
Subject Index
413
Droits d'auteur

Autres éditions - Tout afficher

Introduction to Topological Manifolds
John Lee
Aucun aperçu disponible - 2010
Introduction to Topological Manifolds
John M. Lee
Aucun aperçu disponible - 2011
Introduction to Topological Manifolds
John Lee
Aucun aperçu disponible - 2013

Expressions et termes fréquents

abelian group affine algebraic arbitrary automorphism base point basis bijective called Chapter characteristic property circle closed map lemma closed subset component compute connected sum connectedness construction contained continuous map Corollary covering map CW complex defined definition deformation retraction denote dimension disjoint union disk edge element equivalence class equivalence relation Example Exercise exists fiber field first follows free abelian free group free product function fundamental group given group G Hausdorff space homeomorphic identified ifand induced infinite cyclic injective integer intersection inverse isomorphism lift locally compact locally Euclidean locally finite loop map f map q metric space morphism n-cell n-manifold neighborhood nonempty notation open cover open subset pair path-connected path-homotopic plane polygonal Problem Proposition prove quotient map quotient space restriction satisfies second countable sequence simplicial complex simply connected singular specific sphere subgroup subspace topology Suppose surjective theory topological group topological space unique vector vertex vertices

À propos de l'auteur (2010)

John M. Lee is a professor of mathematics at the University of Washington. His previous Springer textbooks in the Graduate Texts in Mathematics series include the first edition of Introduction to Topological Manifolds, Introduction to Smooth Manifolds, and Riemannian Manifolds: An Introduction.

Informations bibliographiques

TitreIntroduction to Topological Manifolds
Volume 202 de Graduate Texts in Mathematics
AuteurJohn Lee
Édition2, illustrée
ÉditeurSpringer Science & Business Media, 2010
ISBN1441979409, 9781441979407
Longueur433 pages
  
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