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I wanted to know if anyone had any good introductions on algebraic topology for the theoretical physicist? I am particularly interested in applications to condensed matter physics, but would be happy with any kind of resource -- all my friends and I can find are the more abstract mathematical textbooks and articles.

In terms of relevant background, I am looking for something that assumes basic knowledge of quantum theory, quantum field theory, solid state physics, group theory, abstract algebra, and real analysis.

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The books of Nakahara and Frenkel are two physicists' books that come to mind. Charles Kane himself recommended Nakahara very warmly to physicsts, saying he had studied all he knows about topology from that book.

Personally I prefer the simpler math books. One of which is Bredon's.

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The book by Nakahara, as mentioned in its description, is intended for students of particle physics, gravitation & cosmology, and solid state physics. It covers algebraic topology in its first few chapters at a level that is relatively adequate for a physicist. The few knowledgeable people I asked recommended it as a good starting point for topology, and algebraic topology in particular.

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