The second edition is here!
From the back cover:
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. 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. It should be accessible to any student who has completed a solid undergraduate degree in mathematics. The author’s book Introduction to Smooth Manifolds is meant to act as a sequel to this book.
- Table of Contents
- Sample chapter
- Corrections to the book (updated 7/19/2015)
- Please send corrections or suggestions to firstname.lastname@example.org. Be sure to tell me which edition you're writing about. Thanks!
- If you're affiliated with a university that has a subscription to Springer's GTM series, you can read the book online.
About the first edition:
- The first edition (© 2000) is still available in hardcover from some sources. (But it's more expensive and not nearly as good as the second edition!)
- Corrections to the first edition (updated 9/16/2011)