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Viser: Introduction to Topological Manifolds
Introduction to Topological Manifolds Vital Source e-bog
John Lee
(2010)
Introduction to Topological Manifolds
John M. Lee
(2010)
Sprog: Engelsk
Detaljer om varen
- 2. Udgave
- Vital Source searchable e-book (Fixed pages)
- Udgiver: Springer Nature (December 2010)
- ISBN: 9781441979407
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Detaljer om varen
- 2. Udgave
- Hardback: 452 sider
- Udgiver: Springer New York (December 2010)
- ISBN: 9781441979391
This book is an introduction to manifolds at the beginning graduate level, and accessible to any student who has completed a solid undergraduate degree in mathematics. 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.
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.
- 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.