most recent 30 from http://mathoverflow.net 2013-05-22T03:34:20Z http://mathoverflow.net/feeds/question/32198 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/32198/textbook-or-lecture-notes-in-topological-k-theory Martin Pinsonnault 2010-07-16T16:09:10Z 2011-09-12T17:53:22Z

<p>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. </p> <p>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 ?</p>

http://mathoverflow.net/questions/32198/textbook-or-lecture-notes-in-topological-k-theory/32203#32203 Efton Park 2010-07-16T17:10:46Z 2010-07-16T17:10:46Z

<p>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.</p>

http://mathoverflow.net/questions/32198/textbook-or-lecture-notes-in-topological-k-theory/32204#32204 Andrew L 2010-07-16T17:11:31Z 2010-07-16T17:19:12Z

<p>The standard texts on the subject are by Michael Atiyah and Max Karoubi, both called <em>K-Theory</em>,I believe. The Atiyah book is more readable and has fewer prerequisites,but the Karoubi book covers a great deal more. </p>

http://mathoverflow.net/questions/32198/textbook-or-lecture-notes-in-topological-k-theory/32207#32207 userN 2010-07-16T17:33:44Z 2010-07-16T17:33:44Z

<p>I don't know of a single book that does what you want. Perhaps that's because it's hard to top Atiyah &amp; Segal's writings. Pity that Atiyah's book is so expensive. On the other hand, Segal's <a href="http://www.springerlink.com/content/p0455j88250n2424/fulltext.pdf" rel="nofollow">paper</a> on equivariant K-theory is freely available. </p>

http://mathoverflow.net/questions/32198/textbook-or-lecture-notes-in-topological-k-theory/32209#32209 Dan Ramras 2010-07-16T17:40:55Z 2010-07-16T17:40:55Z

<p>I have lecture notes on my <a href="http://www.math.nmsu.edu/~ramras/601.html" rel="nofollow"> website</a> that you might find helpful. They're from a one-semester graduate course (the second such course I've taught). Sadly, they're not yet typed...</p> <p>They're a mix of material from Milnor and Stasheff, Hatcher's notes, and Husemoller's book Fibre Bundles. They cover vector bundles and principle bundles, characteristic classes and the Chern Character, and complex Bott periodicity. They don't cover representation rings or real K-theory. (I assume that in mentioning representation rings, you're talking about the Atiyah-Segal Theorem, or at least Atiyah's version for finite groups? I don't know any textbook reference for that.)</p> <p>The proof of Bott periodicity that I give in the notes is a mixture of Hatcher's proof with some observations from Husemoller's book, and it uses the Chern Character to prove that the Bott map is injective. This is nice, because the proof of injectivity in Hatcher's notes (or Atiyah's book) is a bit more complicated that the proof of surjectivity. So if you're covering the Chern character anyway, this is a nice route to take.</p>

http://mathoverflow.net/questions/32198/textbook-or-lecture-notes-in-topological-k-theory/75240#75240 Yan Zou 2011-09-12T17:53:22Z 2011-09-12T17:53:22Z

<p>@Efton I should say I like your book. It is a well written one. @Andrew Atiyah's book really needs some work. I don't think it is easier. </p>