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Great first book on algebraic topology. Introduces (co)homology through singular theory. Sales Rank: #1126597 in Books Brand: Brand: Westview Press Published on: 1981-01-22 Original language: English Number of items: 1 Dimensions: 8.60" h x.75" w x 6.00" l, 1.09 pounds Binding: Paperback 320 pages Features Used Book in Good Condition Most helpful customer reviews 6 of 6 people found the following review helpful. An expanded and much improved revision of the book By Moses Ma I think this book is most notable for its emphasis on the Eilenberg-Steenrod axioms for homology theory and for the verification of those axioms for the invariant singular homology theory. Using those results, the author shows how to calculate the homology groups of finite cell complexes (and more generally of a space obtained by adjunction from a known space). This provides all the classical results for spheres, compact surfaces, real, complex and quaternionic projective spaces, lens spaces etc. without going through the more tedious method of simplicial complexes. He was able similarly to prove the well-known duality theorems for manifolds and the Lefschetz Fixed Point Theorem, following ideas of Dold. Anyway, this book begins with the basic theory of the fundamental group and covering spaces; then defines the higher homotopy groups and proves they are abelian, but doesn't go further into that theory. The original book by Greenberg heavily emphasized the algebraic aspect of algebraic topology. Harper's additions in this revision contribute a more geometric flavor to the development, adding many examples, figures and exercises to balance the algebra nicely. Harper also provided slicker proofs of a few of the theorems in the original, and added lots of new material not previously discussed (such as about knots). The result is a nicely balanced presentation of a branch of mathematics that began toward the end of the 19th century and has had pretty spectacular development ever since! 17 of 22 people found the following review helpful. Part 2, Singular Homology Theory is recommended. By O., S.
This text is suitable for students of mathematics without prior knowledge of algebraic topology. The best thing with this is Part 2 which treats singular homology theory. However, you may want to resort to Maunder for an effeective introductin to elelmentary homotopy theory, and to Dold for and intruduction to orientation and duality. 0 of 0 people found the following review helpful. Five Stars By Vitaly Zaderman good See all 3 customer reviews...
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