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Introduction to topological manifolds

Author: John M Lee
Publisher: New York : Springer, ©2011.
Series: Graduate texts in mathematics, 202.
Edition/Format:   eBook : Document : English : 2nd edView all editions and formats
Summary:
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  Read more...
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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.
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Abstract:

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.  Read more...

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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. Read more...

 
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