内容简介

This book is intended to serve as a textbook for a course in algebraic topology　at the beginning graduate level. The main topics covered are the classification　of compact 2-manifolds, the fundamental group, covering spaces, singular　homology theory, and singular cohomology theory (including cup products　and the duality theorems of Poincare and Alexander). It consists of material　from the first five chapters of the author's earlier book Algebraic Topology:　An Introduction (GTM 56) together with almost all of his book Singular　Homology Theory (GTM 70). This material from the two earlier books has　been revised, corrected, and brought up to date. There is enough here for a　full-year course.
The author has tried to give a straightforward treatment of the subject　matter, stripped of all unnecessary definitions, terminology, and technical　machinery. He has also tried, wherever feasible, to emphasize the geometric　motivation behind the various concepts. Several applications of the methods　of algebraic topology to concrete geometrical-topological problems are given　(e.g., Brouwer fixed point theorem, Brouwer-Jordan separation theorem,　lnvariance of Domain. Borsuk-Ulam theoremS.