Introduction to Algebraic Topology

Science & Math

Andrew H. Wallace

Mathematics

Pergamon Press, Inc.

Keeping mathematical prerequisites to a minimum, this undergraduate-level text stimulates students' intuitive understanding of topology while avoiding the more difficult subtleties and technicalities. Its focus is the method of spherical modifications and the study of critical points of functions on manifolds. No previous knowledge of topology is necessary for this text, which offers introductory material regarding open and closed sets and continuous maps in the first chapter. Succeeding chapters discuss the notions of differentiable manifolds and maps and explore one of the central topics of differential topology, the theory of critical points of functions on a differentiable manifold. Additional topics include an investigation of level manifolds corresponding to a given function and the concept of spherical modifications. The text concludes with applications of previously discussed material to the classification problem of surfaces and guidance, along with suggestions for further reading and study.

Differential Topology: First Steps (Dover Books on Mathematics)

Dover Publications

This self-contained treatment of algebraic topology assumes only some knowledge of real numbers and real analysis. The first three chapters focus on the basics of point-set topology, offering background to students approaching the subject with no previous knowledge. Readers already familiar with point-set topology can proceed directly to Chapter 4, which examines the fundamental group as well as homology groups and continuous mapping, barycentric subdivision and excision, the homology sequence, and simplicial complexes. Exercises form an integral part of the text; they include theorems that are as valuable as some of those whose proofs are given in full. Author Andrew H. Wallace, Professor Emeritus at the University of Pennsylvania, concludes the text with a guide to further reading.

An Introduction to Algebraic Topology (Dover Books on Mathematics)

This self-contained text is suitable for advanced undergraduate and graduate students and may be used either after or concurrently with courses in general topology and algebra. It surveys several algebraic invariants: the fundamental group, singular and Cech homology groups, and a variety of cohomology groups. Proceeding from the view of topology as a form of geometry, Wallace emphasizes geometrical motivations and interpretations. Once beyond the singular homology groups, however, the author advances an understanding of the subject's algebraic patterns, leaving geometry aside in order to study these patterns as pure algebra. Numerous exercises appear throughout the text. In addition to developing students' thinking in terms of algebraic topology, the exercises also unify the text, since many of them feature results that appear in later expositions. Extensive appendixes offer helpful reviews of background material.

Algebraic Topology: Homology and Cohomology (Dover Books on Mathematics)

See the best price to sell, buy, or rent books by Andrew H. Wallace. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Andrew H. Wallace

See the best price to sell, buy, or rent books by Andrew H. Wallace. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Introduction to Algebraic Topology

Differential Topology: First Steps (Dover Books on Mathematics)

An Introduction to Algebraic Topology (Dover Books on Mathematics)

Algebraic Topology: Homology and Cohomology (Dover Books on Mathematics)