Algebraic Topology: Homology and Cohomology (Dover Books on Mathematics) by Andrew H. Wallace (PDF)

Description

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.

User’s Reviews

Editorial Reviews: About the Author Andrew H. Wallace is Professor Emeritus of Mathematics at the University of Pennsylvania and the author of two other Dover books.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This graduate-level 1970 book by Andrew Hugh Wallace (1926-2008) is the natural sequel to the author’s easy introduction for beginners, ”

⭐”. So it’s a good idea to read that book first!The author covers singular homology groups, cohomology groups, cohomology rings, Čech homology groups, and Čech cohomology theory. This book has all of the complexity that was absent in the easy introduction! There’s a good year of graduate level study in this book, whereas the author’s earlier Introduction could be easily finished in a week of bedtime reading.

⭐This book claims to have no prerequisites other than general topology and algebra, and implies that even these can be taken concurrently. But in reality it assumes more advanced knowledge. For example, it talks about cell complexes without even defining them. It also has unclear definitions, confusing notation and many notational errors.

Keywords

Free Download Algebraic Topology: Homology and Cohomology (Dover Books on Mathematics) in PDF format
Algebraic Topology: Homology and Cohomology (Dover Books on Mathematics) PDF Free Download
Download Algebraic Topology: Homology and Cohomology (Dover Books on Mathematics) 2007 PDF Free
Algebraic Topology: Homology and Cohomology (Dover Books on Mathematics) 2007 PDF Free Download
Download Algebraic Topology: Homology and Cohomology (Dover Books on Mathematics) PDF
Free Download Ebook Algebraic Topology: Homology and Cohomology (Dover Books on Mathematics)