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 | | Homology Theory: An Introduction to Algebraic Topology (Graduate Texts in Mathematics) (v. 145) by James W. Vick ISBN-10: 9780387941264 ISBN-10: 0-387-94126-6 ISBN-13: 9780387941264 ISBN-13: 978-0-387-94126-4 Hardcover 1994-01-07 Springer Find Lowest Price |
Editorials | ||
Product Description Designed to be an introduction to some of the basic ideas in the field of algebraic topology. Devoted to the foundations and applications of homology theory. DLC: Homology theory. | ||
Reviews | ||
(Co)Homology the Way it Should Be This was the textbook for the first third of a year-long algebraic topology sequence at Oregon State in 1973-4. We were told by the prof that Vick was a student of Stong and that the book was essentially Stong's course written up with his blessing. It's hard to ask for a better pedigree than that, as Stong was a legend for his teaching (as well as his research). Although there are some minor quibbles (noted in the 4-star reviews), I still haven't found a better treatment of the key results, nor a more direct path. The proof of Poincare duality in particular is that of Hans Samelson, another legend in the field for both teaching and research. Checking the references, one finds that this was not the only such example where Vick sought out what was then regarded as the best proof available for beginners. It is also noteworthy that community consensus on which are best has not changed much, if any, since then. The plethora of typos may be a "feature" of the reprint, since I don't recall that many in the original Acad. Press edition we used, and I still have. As should be clear, this one is a real keeper. For more modern/advanced study, continue with Switzer and Brayton Gray. By then the journals should be reasonably accessible. | ||
Has the good and bad This is a terrific book on homology theory, covering all the standard topics, plus some nice topics that are hard to find in other introductory books. The motivation for theory is presented in both algebraic/categorical and geometric flavors. The structure of the book is mostly solid, getting straight to the point with singular homology instead of wasting time with simplicial homology and its results (a rarity with algebraic topology books). My only complaints are that the book is riddled with typos and chapter 5 (on products in homology and cohomology) is quite messy. | ||
Masterful This introduction to singular homology combines a strong historical sense with an easy mastery of modern methods. The massive contributions of Poincare and Brouwer are credited, and their geometrical motivations are clear. At the same time the book neither minimizes nor apologizes for modern algebraic machinery, but treats categories and acyclic models and more as natural means to simplify the subject. The book goes through Poincare duality and a good account of the Lefschetz fixed point theorems. It is at once very visual and algebraically slick. The only problem with this approach is that the author seems a bit uncomfortable descending into the nuts and bolts of the longer proofs of two key results (the acyclic model theorem, and the duality theorem). He handles the details unevenly and makes some actual mis-statements. Here the reader needs the experience and confidence to make some corections. | ||