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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Editorial Reviews
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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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34 of 34 people found the following review helpful:
5.0 out of 5 stars
Excellent text on algebraic topology,
By A Customer
This review is from: A basic course in algebraic topology (v. 127) (Hardcover)
The text contains material from the author's earlier two books; Algebraic Topology: An Introduction (GTM 56), and Singular Homology Theory (GTM 70). The book starts with an introductory chapter on 2-manifolds and then continues with the fundamental group; which is conceptually easier than homology, with which some books on algebraic topology start. The only prerequisite for this book is a basic knowledge of general topology; and the book is easily accessible to anyone studying on his own. In short, I recommend the book to anyone interested in algebraic topology.
3 of 4 people found the following review helpful:
5.0 out of 5 stars
Good for newbies,
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This review is from: A basic course in algebraic topology (v. 127) (Hardcover)
Very nice way to start learning Alg topology. I am reading it for a class and it's been quite pleasant.
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The topological concept of a surface or 2-dimensional manifold is a mathematical abstraction of the familiar concept of a surface made of paper, sheet metal, plastic, or some other thin material. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Princeton University Press, Two-Dimensional Manifolds, Seifert-Van Kampen, Academic Press, Mac Lane, Textbook of Topology, Alexander-Spanier Cochains, Homogeneous G-spaces, Marcel Dekker, Combinatorial Group Theory, First Application of Theorem, Lifting of Arbitrary Maps, Permutation Groups, The University Press New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The topological concept of a surface or 2-dimensional manifold is a mathematical abstraction of the familiar concept of a surface made of paper, sheet metal, plastic, or some other thin material. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Princeton University Press, Two-Dimensional Manifolds, Seifert-Van Kampen, Academic Press, Mac Lane, Textbook of Topology, Alexander-Spanier Cochains, Homogeneous G-spaces, Marcel Dekker, Combinatorial Group Theory, First Application of Theorem, Lifting of Arbitrary Maps, Permutation Groups, The University Press New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
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100
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- Algebraic Topology (Colloquium Pbns. Series, Vol 27) by Solomon Lefschetz on page 157, page 322, and page 349
- Algebraic Number Theory (Graduate Texts in Mathematics) by Serge Lang in Back Matter (1), Back Matter (2), and Back Matter (3)
- Algebraic Topology by Edwin H. Spanier on page 146, page 303, and page 392
- Homotopy Theory by George W. Whitehead in Front Matter, page 253, and page 406
- Lectures on Algebraic Topology (Classics in Mathematics) by Albrecht Dold on page 303, page 349, and page 392
See all 100 books this book cites
- Graph Coloring Problems (Wiley Series in Discrete Mathematics and Optimization) by Tommy R. Jensen on page 28, and page 249
- Algebraic Topology by William Fulton in Back Matter (1), and Back Matter (2)
- Probability Theory II (Graduate Texts in Mathematics) by M. Loeve in Back Matter
- Foundations of Hyperbolic Manifolds (Graduate Texts in Mathematics) by John G. Ratcliffe in Back Matter
- Galois Theory (Graduate Texts in Mathematics) by Harold M. Edwards in Back Matter
See all 100 books citing this book
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