拓扑流形引论 内容简介

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. 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 manifolds; the remaining two-thirds focuses on smooth manifolds.

拓扑流形引论 本书特色

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！

拓扑流形引论 目录

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