### W.S. MASSEY, Yale University, New Haven,
CT

## A Basic Course in Algebraic Topology

*"In the minds of many people algebraic topology is a subject
which is esoteric,
specialized, and disjoint from the overall sweep of mathematical
thought. 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."*

-G. Ellis, University College, Galaway, Bulletin of the Irish Mathematics Society

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.

*Contents:* * 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 in Manifolds * Cup Products in Projective Spaces and
Applications of Cup
Products * A Proof of De Rham's Theorem * Permutation Groups or
Transformation
Groups

**1991/428 PP., 57 ILLUS./HARDCOVER/$54.95/ISBN
0-387-97430-X**

GRADUATE TEXTS IN MATHEMATICS, VOLUME 127

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