K Theory: Book Recommendations

Question

Good people!

So I've been hoping to get into K Theory for a while now, and the book that I have been trying to use (and failing) has been Charles Weibel's book by that very title.

The book itself isn't bad, but it's not for the faint-hearted, and can appear quite dense and challenging to a relative newbie like me. As such, I was wondering if someone might be able to recommend a book or two or three or $n$ to help "ease" my way into Weibel. Something that touches upon the constructions he introduces in the first chapter--Picard groups, topological and algebraic vector bundles, Chern classes, etc.--but being more, well, easy for a newbie to process.

I look forward to your suggestions.

Answer 1

From just as much of a newbie, I'd recommend you these notes by Eric Friedlander to begin with.

I'm personally also fond of this introductive article by Inna Zakharevich.

Coming to... larger books, I'm not really aware of any "easier" reference than Weibel's, so I think I'll leave recommendations to users way more expert than me on the subject.

Answer 2

Personally, I like: An Algebraic Introduction to K-Theory , Bruce A. Magurn

https://www.cambridge.org/an/academic/subjects/mathematics/algebra/algebraic-introduction-k-theory?format=HB&isbn=9780521800785

THis is suitable for beginners, with lot of interesting sources of $K_0$ and $K_1$, and classical theorems (such as excision exact sequences)

Answer 3

Other than the above recommendations, I would also recommend this paper by Grayson, which gives a big picture overview of Quillen's $K$-theory.

If and when you can understand Grayson's papers above, I would highly recommend Quillen's original paper Higher algebraic K-theory I. While it is certainly not for beginners, I think it still is something which is quite readable with the correct background.