An Introduction to Algebraic Topology

Graduate Texts in Mathematics #119

by Joseph J. Rotman

A clear exposition, with exercises, of the basic ideas of algebraic topology. Suitable for a two-semester course at the beginning graduate level, it assumes a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced.

Genres: Mathematics, Textbooks, Algebra

451 pages, Hardcover

First published August 17, 1988

Reviews

[Jonathan · Rating 3 out of 5]

A reasonably clear introduction to algebraic topology, including many technical details that Hatcher leaves for the reader or relegates to the appendices (I'm think CW-complexes here). Thus Rotman's book is very suitable for reading along side Hatcher, or as very first and gentler introduction.

Hatcher has much better exposition, giving a better overview, more intuition, and better introductions to the topics in algebraic topology that he covers. Rotman's introductions are short and more bare of examples and reasons to care about what he is about to introduce. Hatcher also includes many more applications of algebraic topology, as well as introductions to more advanced topics, but Rotman still proves some interesting things, like using homology to prove the hairy ball theorem.

Let me be clear, Rotman's book is not bad, it does what it claims to do: provide an introduction to algebraic topology, it's just not as good as the best introductory books that I've read. For example: Tu's "An Introduction To Manifolds", Abbott's "Understanding Analysis", or Lee's "An Introduction To Smooth Manifolds". Perhaps what I'm trying to say is that: it's a fine introduction if you don't have good lectures to go along with Hatcher, or are not dedicated/motivated enough to go through all the details in Hatcher yourself.

[curtis · Rating 5 out of 5]

I found it much more suitable than Hatcher. Doesn't skip details the way other introductions to algebraic topology do, or at least spells out which parts it assumes. I tend to like Rotman's approach in particular and this is no exception.