Introduction to Topological Manifolds

John M. Lee is a professor of mathematics at the University of Washington. His previous Springer textbooks in the Graduate Texts in Mathematics series include the first edition of Introduction to Topological Manifolds, Introduction to Smooth Manifolds, and Riemannian Manifolds: An Introduction.

• 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.

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)