Algebraic Topology: A First Course 1st Edition by Marvin J. Greenberg (PDF)

Description

Great first book on algebraic topology. Introduces (co)homology through singular theory.

User’s Reviews

Editorial Reviews: About the Author Marvin J Greenberg

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

⭐The text looks like a poor quality photocopy. It’s annoyingly blurry and in some places unreadable. It might be well written, but you’ll definitely need another reference if you want to actually make out some of the notation. I’m amazed that CRC can get away with producing such a low quality product. Buyer beware.

⭐good

⭐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!

⭐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.

⭐well, a brand new good book.

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