Introduction to Topological Manifolds

• Main Author: Lee, John M. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2011.
• Series: Graduate Texts in Mathematics, 202
• Subjects: Mathematics.; Algebraic topology.; Manifolds (Mathematics).; Complex manifolds.; Manifolds and Cell Complexes (incl. Diff.Topology).; Algebraic Topology.

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 develo...

Table of Contents:

• Preface
• 1 Introduction
• 2 Topological Spaces
• 3 New Spaces from Old
• 4 Connectedness and Compactness
• 5 Cell Complexes
• 6 Compact Surfaces
• 7 Homotopy and the Fundamental Group
• 8 The Circle
• 9 Some Group Theory
• 10 The Seifert-Van Kampen Theorem
• 11 Covering Maps
• 12 Group Actions and Covering Maps
• 13 Homology
• Appendix A: Review of Set Theory
• Appendix B: Review of Metric Spaces
• Appendix C: Review of Group Theory
• References
• Notation Index
• Subject Index.