Algebraic Topology ─ Homology and Cohomology

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 (professor emeritus, University of Pennsylvania) emphasizes geometrical motivations and interpretations. Once beyond the singular homology groups, he advances an understanding of the subject's algebraic patterns, leaving geometry aside to study these patterns as pure algebra. Exercises are included, and many of them feature results that appear in later expositions. Appendices offer reviews of background material in fundamental groups and general topology. This is an unabridged republication of the edition published by W. A. Benjamin, Inc., New York, 1970. Annotation c2008 Book News, Inc., Portland, OR (booknews.com)