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Catalogue Information
Field name	Details
Dewey Class	514.34
Title	Introduction to Topological Manifolds ([EBook]) / by John M. Lee.
Author	Lee, John M. , 1950-
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer , 2011.
Physical Details	XVIII, 434 pages : online resource.
Series	Graduate texts in mathematics 0072-5285 ; ; 202
ISBN	9781441979407
Summary Note	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 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.Â 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. This text is designed to be used for an introductory graduate course on the geometry and topology of manifolds.Â It should be accessible to any student who has completed a solid undergraduate degree in mathematics.Â The authorâs book Introduction to Smooth Manifolds is meant to act as a sequel to this book.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-1-4419-7940-7
Links to Related Works	Subject References: Algebraic Topology . Cell aggregation . Manifolds and Cell Complexes (incl. Diff.Topology) . Mathematics . Authors: Lee, John M. 1950- . Corporate Authors: SpringerLink (Online service) . Series: Graduate texts in mathematics . GTM . Classification: 514.34 . 514.34 (DDC 23) .

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Introduction to Topological Manifolds

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