**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. |