拓撲流形引論

內(nèi)容概要

本書以英文的形式介紹了拓撲流形引論的內(nèi)容。

書籍目錄

Preface1 Introduction  What Are Manifolds?  Why Study Manifolds?2 Topologiacl Spaces  Topologies  Bases  Manifolds  Problems3 New Spaces form Old  Subspaces  Product Spaces   Quotient Spaces  Group Actions  Problems4 Connectedness and Compactness  Connectedness  Compactness  Locally Compact Hausdorff Spaces  Problems5 Simplicial Complexes  Euclidean Simplicial Complexes  Abstract Simplicial Complexes  Triangulation Theorems  Orientations  Combinatorial Invariants  Problems6 Curves and Surfaces  Classification of Curves  Surfaces  Connected Sums  Polygonal Presentations of Surfaces  Classification of Surface Presentations  Combinatorial Invariants  Problems7 Homotopy and the Fundamental Group  Homotopy  The Fundamental Group  Homomorphisma Induced by Continuous Maps  ……8 Circles and Spheres9 Some Group Theory10 The Seifert-Van Kampen Theorem11 Covering Spaces12 Classification of Coverings13 HomologyAppendix：Review of PrerequisitesReferencesIndex

編輯推薦

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.

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