I am looking for a good introductory level textbook (or set of lecture notes) on classical topological K-Theory that would be suitable for a one-semester graduate course. Ideally, it would require minimal background: standard introductory courses in algebraic topology and differential geometry, would cover core topics (Bott periodicity, Chern character, representation rings, etc) mostly in a self-contained way, and would give interesting examples and exercises.
As I learned the subject from multiple books and papers, I don't know a "canonical" reference that gives a coherent picture of the subject. Any suggestions ?
Best Answer
I wrote a book that may be what you are looking for. It's called "Complex Topological K-Theory," and it is published by Cambridge University Press. As the title suggests, I do not discuss real (KO) theory in the book, and I also do not talk about representation rings. But the other topics you mentioned are covered, and the only background required for the book are introductory courses in point-set topology and abstract algebra.