Vector Bundles & K-Theory
The plan is for this to be a fairly short book focusing on topological K-theory and containing also the necessary background material on vector bundles and characteristic classes. Here is a provisional Table of Contents. At present only about half of the book is in good enough shape to be posted online, approximately 110 pages. This is available as a pdf file here. (I have reformatted this with narrower margins for a better reading experience on devices like an iPad, but for a paper copy with more standard size margins try printing at 85-90 per cent of full size.)
What is included in this installment is:
Much of this material is already well covered in other sources, notably the classic books of Atiyah (K-theory) and Milnor & Stasheff (Characteristic Classes). These books are still in print, although they have become somewhat expensive.
Eventually I intend for the book to include things that aren't readily accessible elsewhere, such as the full story on the stable J homomorphism. What is posted now is Version 2.1, dated May 2009. This is a very minor revision of Version 2.0 from January 2003. Unfortunately I haven't been able to find time to work on the book much since then. When I do get back to serious work on it, the first thing I plan to do is extend the proof of Bott periodicity from the complex case to the real case following the argument in Atiyah's book, using Clifford algebras.