K-theory

by Michael Francis Atiyah

K-theory (Advanced Book Classics)

Genres: Mathematics

216 pages, Hardcover

First published July 1, 1989

About the author

Sir Michael Francis was a British-Lebanese mathematician specialising in geometry.

Reviews

[Dow · Rating 4 out of 5]

Pretty poorly written, and the comment in the introduction that this only relies on linear algebra is laughable (unless that's where you learned homotopy theory...). With that aside, everything is pretty elementary, which makes this The Book on K-theory. Anyone who wants to learn the K-Theory proof of complex Bott Periodicity ought to read this book first (one should also read Milnor's Morse Theory, which contains Bott's original, beautiful, proof as well as an extension to the real case due to Atiyah, Bott, and Shapiro) to avoid ultra-modern treatments using Fredholm operators and all of that. That stuff is meant to prepare the reader for the K-Theoretic proof of the Atiyah-Singer index theorem; this is a proof which is great to know, but certainly would make a first pass at K-theory far harder than it need be.