| This book is an introduction to manifolds at the beginning graduate level:It contains the essential topological ideas that are needed for the furtherstudy 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. Here at the University of Washington, for example, this text is used for the first third of a year-long course on the geometry and topology of anifolds; the remaining two-thirds focuses on smooth manifolds. 此书为英文版！ |
| Preface 1 Introduction What Are Manifolds? Why Study Manifolds? 2 Topologiacl Spaces Topologies Bases Manifolds Problems 3 New Spaces form Old Subspaces Product Spaces Quotient Spaces Group Actions Problems 4 Connectedness and Compactness Connectedness Compactness Locally Compact Hausdorff Spaces Problems 5 Simplicial Complexes Euclidean Simplicial Complexes Abstract Simplicial Complexes Triangulation Theorems Orientations Combinatorial Invariants Problems 6 Curves and Surfaces Classification of Curves Surfaces Connected Sums Polygonal Presentations of Surfaces Classification of Surface Presentations Combinatorial Invariants Problems 7 Homotopy and the Fundamental Group Homotopy The Fundamental Group Homomorphisma Induced by Continuous Maps …… 8 Circles and Spheres 9 Some Group Theory 10 The Seifert-Van Kampen Theorem 11 Covering Spaces 12 Classification of Coverings 13 Homology Appendix：Review of Prerequisites References Index |
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