A Basic Course in Algebraic Topology

Hardcover | 6 March 1991 | Edition Number 3

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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. These topics are developed systematically, avoiding all unecessary definitions, terminology, and technical machinery. Wherever possible, the geometric motivation behind the various concepts is emphasized. The text 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 the now out-of- print SINGULAR HOMOLOGY THEORY (GTM 70). The material from the earlier books has been carefully revised, corrected, and brought up to date.

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W.S. Massey

A Basic Course in Algebraic Topology

"In the minds of many people algebraic topology is a subject which is a ~esoteric, specialized, and disjoint from the overall sweep of mathematical thought.a (TM) This straightforward introduction to the subject, by a recognized authority, aims to dispel that point of view by emphasizing: 1. the geometric motivation for the various concepts and 2. the applications to other areas."a "BULLETIN OF THE IRISH MATHEMATICS SOCIETY

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Two-Dimensional Manifolds
The Fundamental Group
Free Groups and Free Products of Groups
Seifert and Van Kampen Theorem on the Fundamental Group of the Union of Two Spaces. Applications
Covering Spaces
Background and Motivation for Homology Theory
Definitions and Basic Properties of Homology Theory
Determination of the Homology Groups of Certain Spaces: Applications and Further Properties of Homology Theory
Homology of CW-Complexes
Homology with Arbitrary Coefficient Groups
The Homology of Product Spaces
Cohomology Theory
Products in Homology and Cohomology
Duality Theorems for the Homology of Manifolds
Cup Products in Projective Spaces and Applications of Cup Products
A Proof of De Rham's Theorem
Permutation Groups or Tranformation Groups
Table of Contents provided by Publisher. All Rights Reserved.

A Basic Course in Algebraic Topology

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