Synopses & Reviews
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.
Synopsis
This self-contained treatment 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. 1970 edition.
Synopsis
This self-contained treatment studies several algebraic invariants: the fundamental group, singular and Cech homology groups, and a variety of cohomology groups. Extensive appendixes review background material. 1970 edition.
About the Author
Andrew H. Wallace is Professor Emeritus of Mathematics at the University of Pennsylvania and the author of two other Dover books.
Table of Contents
Preface1. Singular Homology Theory2. Singular and Simplicial Homology3. Chain ComplexesHomology and Cohomology4. The Cohomology Ring5. Cech Homology TheoryThe Construction6. Further Properties of Cech Homology Theory7. Cech Cohomology TheoryAppendix A. The Fundamental GroupAppendix B. General TopologyBibliographyIndex