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Genre/Form: | Electronic books |
---|---|
Additional Physical Format: | Print version: Lee, John M., 1950- Introduction to topological manifolds. New York : Springer, ©2011 (OCoLC)695533618 |
Material Type: | Document, Internet resource |
Document Type: | Internet Resource, Computer File |
All Authors / Contributors: |
John M Lee |
ISBN: | 9781441979407 1441979409 |
OCLC Number: | 697506452 |
Description: | 1 online resource (xvii, 433 pages) : illustrations |
Contents: | Machine generated contents note: 1. Introduction -- What Are Manifolds? -- Why Study Manifolds? -- 2. Topological Spaces -- Topologies -- Convergence and Continuity -- Hausdorff Spaces -- Bases and Countability -- Manifolds -- Problems -- 3. New Spaces from Old -- Subspaces -- Product Spaces -- Disjoint Union Spaces -- Quotient Spaces -- Adjunction Spaces -- Topological Groups and Group Actions -- Problems -- 4. Connectedness and Compactness -- Connectedness -- Compactness -- Local Compactness -- Paracompactness -- Proper Maps -- Problems -- 5. Cell Complexes -- Cell Complexes and CW Complexes -- Topological Properties of CW Complexes -- Classification of 1-Dimensional Manifolds -- Simplicial Complexes -- Problems -- 6. Compact Surfaces -- Surfaces -- Connected Sums of Surfaces -- Polygonal Presentations of Surfaces -- Classification Theorem -- Euler Characteristic -- Orientability -- Problems -- 7. Homotopy and the Fundamental Group -- Homotopy -- Fundamental Group -- Homomorphisms Induced by Continuous Maps -- Homotopy Equivalence -- Higher Homotopy Groups -- Categories and Functors -- Problems -- 8. Circle -- Lifting Properties of the Circle -- Fundamental Group of the Circle -- Degree Theory for the Circle -- Problems -- 9. Some Group Theory -- Free Products -- Free Groups -- Presentations of Groups -- Free Abelian Groups -- Problems -- 10. Seifert-Van Kampen Theorem -- Statement of the Theorem -- Applications -- Fundamental Groups of Compact Surfaces -- Proof of the Seifert-Van Kampen Theorem -- Problems -- 11. Covering Maps -- Definitions and Basic Properties -- General Lifting Problem -- Monodromy Action -- Covering Homomorphisms -- Universal Covering Space -- Problems -- 12. Group Actions and Covering Maps -- Automorphism Group of a Covering -- Quotients by Group Actions -- Classification Theorem -- Proper Group Actions -- Problems -- 13. Homology -- Singular Homology Groups -- Homotopy Invariance -- Homology and the Fundamental Group -- Mayer-Vietoris Theorem -- Homology of Spheres -- Homology of CW Complexes -- Cohomology -- Problems -- Appendix A Review of Set Theory -- Basic Concepts -- Cartesian Products, Relations, and Functions -- Number Systems and Cardinality -- Indexed Families -- Appendix B Review of Metric Spaces -- Euclidean Spaces -- Metrics -- Continuity and Convergence -- Appendix C Review of Group Theory -- Basic Definitions -- Cosets and Quotient Groups -- Cyclic Groups. |
Series Title: | Graduate texts in mathematics, 202. |
Responsibility: | John M. Lee. |
More information: |
Abstract:
Reviews
Publisher Synopsis
From the reviews of the second edition:"An excellent introduction to both point-set and algebraic topology at the early-graduate level, using manifolds as a primary source of examples and motivation. ... The author has ... fulfilled his objective of integrating a study of manifolds into an introductory course in general and algebraic topology. This text is well-organized and clearly written, with a good blend of motivational discussion and mathematical rigor. ... Any student who has gone through this book should be well-prepared to pursue the study of differential geometry ... ." (Mark Hunacek, The Mathematical Association of America, March, 2011)"This book is designed for first year graduate students as an introduction to the topology of manifolds. ... The book can be read with advantage by any graduate student with a good undergraduate background, and indeed by many upper class undergraduates. It can be used for self study or as a text book for a fine geometrically flavored introduction to manifolds. One which provides excellent motivation for studying the machinery needed for more advanced work." (Jonathan Hodgson, Zentralblatt MATH, Vol. 1209, 2011) Read more...


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by bstatton updated 2017-11-28