This textbook is intended 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 unnecessary definitions, terminology, and technical machinery. 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 his book, Singular Homology Theory 1991st Edition (GTM 70). The material from the two earlier books has been substantially revised, corrected, and brought up to date.
Editorial Reviews
Review
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
W.S. Massey
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.”BULLETIN OF THE IRISH MATHEMATICS SOCIETY
From the Back Cover
This textbook is intended 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 unnecessary definitions, terminology, and technical machinery. 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 his book, Singular Homology Theory 1991st Edition (GTM 70). The material from the two earlier books has been substantially revised, corrected, and brought up to date.
About the Author
William S. Massey (1920-2017) was an American mathematician known for his work in algebraic topology. The Blakers-Massey theorem and the Massey product were both named for him. His textbooks Singular Homology Theory 1991st Edition and Algebraic Topology: An Introduction are also in the Graduate Texts in Mathematics series.
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