Holdings: Introduction to topological manifolds

Introduction to topological manifolds:

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Bibliographic Details
Main Author:	Lee, John M. 1950- (Author)
Format:	Book
Language:	English
Published:	New York, NY Springer [2011]
Edition:	Second edition
Series:	Graduate texts in mathematics 202
Subjects:	Topologische Mannigfaltigkeit
Online Access:	Inhaltsverzeichnis
Physical Description:	xvii, 433 Seiten Illustrationen, Diagramme
ISBN:	9781441979391 9781461427902

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MARC


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adam_text	Contents Preface ............................................................ v 1 Introduction ................................................... 1 What Are Manifolds? ............................................ 1 Why Study Manifolds? ........................................... 4 2 Topological Spaces ............................................. 19 Topologies ..................................................... 19 Convergence and Continuity ...................................... 26 Hausdorff Spaces ............................................... 31 Bases and Countability ........................................... 33 Manifolds ...................................................... 38 Problems ...................................................... 45 3 New Spaces from Old ........................................... 49 Subspaces ..................................................... 49 Product Spaces ................................................. 60 Disjoint Union Spaces ........................................... 64 Quotient Spaces ................................................ 65 Adjunction Spaces .............................................. 73 Topological Groups and Group Actions ............................. 77 Problems ...................................................... 81 4 Connectedness and Compactness ................................ 85 Connectedness .................................................. 86 Compactness ................................................... 94 Local Compactness .............................................. 104 Paracompactness ................................................ 109 Proper Maps ................................................... 1 8 Problems ...................................................... 122 xvj Contents 5 Cell Complexes ................................................127 Cell Complexes and CW Complexes ...............................127 Topological Properties of CW Complexes ...........................135 Classification of 1 -Dimensional Manifolds ..........................143 Simplicial Complexes ............................................147 Problems ......................................................155 6 Compact Surfaces ..............................................159 Surfaces .......................................................159 Connected Sums of Surfaces ......................................164 Polygonal Presentations of Surfaces ................................166 The Classification Theorem .......................................173 The Euler Characteristic ..........................................178 Orientability ...................................................180 Problems ......................................................181 7 Homotopy and the Fundamental Group ..........................183 Homotopy .....................................................184 The Fundamental Group .........................................186 Homomorphisms Induced by Continuous Maps ......................197 Homotopy Equivalence ..........................................200 Higher Homotopy Groups ........................................208 Categories and Functors ..........................................209 Problems ......................................................214 8 The Circle .....................................................217 Lifting Properties of the Circle ....................................218 The Fundamental Group of the Circle ..............................224 Degree Theory for the Circle ......................................227 Problems ......................................................230 9 Some Group Theory ............................................233 Free Products ...................................................233 Free Groups ....................................................239 Presentations of Groups ..........................................241 Free Abelian Groups .............................................244 Problems ......................................................248 10 The Seifert-Van Kampen Theorem ...............................251 Statement of the Theorem ........................................251 Applications ...................................................255 Fundamental Groups of Compact Surfaces ..........................264 Proof of the Seifert-Van Kampen Theorem ..........................268 Problems ......................................................273 Contents xvii 11 Covering Maps ................................................277 Definitions and Basic Properties ...................................278 The General Lifting Problem ......................................283 The Monodromy Action ..........................................287 Covering Homomorphisms .......................................294 The Universal Covering Space ....................................297 Problems ......................................................302 12 Group Actions and Covering Maps ...............................307 The Automorphism Group of a Covering ............................308 Quotients by Group Actions ......................................311 The Classification Theorem .......................................315 Proper Group Actions ............................................318 Problems ......................................................334 13 Homology .....................................................339 Singular Homology Groups .......................................340 Homotopy Invariance ............................................347 Homology and the Fundamental Group .............................351 The Mayer-Vietoris Theorem .....................................355 Homology of Spheres ............................................364 Homology of CW Complexes .....................................369 Cohomology ...................................................374 Problems ......................................................379 Appendix A: Review of Set Theory ...................................381 Basic Concepts .................................................381 Cartesian Products, Relations, and Functions ........................384 Number Systems and Cardinality ..................................390 Indexed Families ................................................391 Appendix B: Review of Metric Spaces ................................395 Euclidean Spaces ...............................................395 Metrics ........................................................396 Continuity and Convergence ......................................398 Appendix C: Review of Group Theory ................................401 Basic Definitions ................................................401 Cosets and Quotient Groups ......................................403 Cyclic Groups ..................................................405 References .........................................................407 Notation Index .....................................................409 Subject Index ......................................................413
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spelling	Lee, John M. 1950- Verfasser (DE-588)122260880 aut Introduction to topological manifolds John M. Lee Second edition New York, NY Springer [2011] © 2011 xvii, 433 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 202 Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd rswk-swf Topologische Mannigfaltigkeit (DE-588)4185712-4 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4419-7940-7 Graduate texts in mathematics 202 (DE-604)BV000000067 202 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021145981&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Lee, John M. 1950- Introduction to topological manifolds Graduate texts in mathematics Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd
subject_GND	(DE-588)4185712-4
title	Introduction to topological manifolds
title_auth	Introduction to topological manifolds
title_exact_search	Introduction to topological manifolds
title_full	Introduction to topological manifolds John M. Lee
title_fullStr	Introduction to topological manifolds John M. Lee
title_full_unstemmed	Introduction to topological manifolds John M. Lee
title_short	Introduction to topological manifolds
title_sort	introduction to topological manifolds
topic	Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd
topic_facet	Topologische Mannigfaltigkeit
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