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Since characteristic classes and index theorems are occasionally used in quantum field theory (for example, when discussing instantons or quantum anomalies), I want to learn more about them. Is there any good textbook available where I can read about index theorems and the theory of characteristic classes?

I'm not looking for advanced mathematical literature written for mathematicians. I need a book that is relatively accessible to physicists and provides at least semi-rigorous proofs of the statements.

The only book of this type I know is Nakahara's Geometry, Topology and Physics. I read it but didn't like it because the author gives lots of formal definitions without prior motivation and when discussing index theorems he doesn't even try to prove anything. Are there any better alternatives to Nakahara?

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  • $\begingroup$ I actually think Tu's book "Differential Geometry" is good, but you'll need to read the prequel by the same author ("An introduction to manifolds") if you have no diff geom background, but you probably do. It doesn't go as far as Atiyah-Singer, but you'll have a good foundation after reading it. It's a maths book, so proofs are given. $\endgroup$
    – Frido
    Commented Sep 28, 2023 at 13:59

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