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I'm mainly interested (graduate student) in surgery theory and geometric topology.

If I have a chance to suggest "must read" papers in geometric topology for beginner, I'm very glad to suggest "Topological Library" books volume 1,2,3 (including monumental papers of Smale,Milnor,Kervaire-Milnor,Thom,Serre,Novikov...) available in the following cite.(volume 3 is not available in English edition up to now)

http://www.amazon.com/Topological-Library-Characteristic-Structures-Everything/dp/9812836861/ref=sr_1_1?s=books&ie=UTF8&qid=1296894607&sr=1-1

Question: What are "must read" papers in algebraic K-theory? (I hope that most of them can be readable with basic understanding about classical K-theory such as Rosenberg's text or Milnor's ann. math. studies book)

edited Feb 5 2011 at 21:19

Mikhail Bondarko

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3 revisions, 2 users
Topologieee 100%

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Only tangentially related, but Lurie is giving a course on surgery theory and L-theory, which might have to do with what you're looking for. He has course notes on his website. – Harry Gindi Feb 5 2011 at 12:58

Warning, it does use a fair bit of black magic, but somehow, as far as I've seen, nothing makes essential use of results from HTT or DAG I. – Harry Gindi Feb 5 2011 at 13:08

Thanks Harry! I did not see that, and I am taking a course on surgery this semester, thes will be fun to compare with my notes. – Sean Tilson Feb 6 2011 at 4:58

@Harry: Lurie's course does not even mention K-theory. It is on L-theory; a completely different story. – Johannes Ebert Jul 23 at 9:44

Steven Landsburg · Answer 1 · 2012-07-22 18:08:10Z UTC

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The first few sections of the Thomason/Trobaugh paper constitute an exceptionally readable overview of the Waldhausen approach to K-theory, with very few prerequisites.

answered Jul 22 at 18:08

Steven Landsburg

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Steven, could you give a (more) complete reference? – Ryan Budney Jul 23 at 0:33

I see there's two, one you reviewed on MathSciNet and one reviewed by Weibel. – Ryan Budney Jul 23 at 0:37

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Ryan Budey: I meant the paper "Higher Algebraic K-Theory of Schemes and of Derived Categories", published in the Grothendieck Festschrift (and apparently unavailable online). I forget whether this is the one I reviewed. I've just spent a couple of hours refreshing my memory of this paper, and I've been reminded anew that there is major enlightenment in every section. I would not hesitate to recommend this to a novice (with a good first-year graduate education); it covers a fantastic amount of ground and is amazingly easy to read. – Steven Landsburg Jul 23 at 1:57

K.J. Moi · Answer 2 · 2011-02-05 14:59:48Z UTC

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Algebraic K-theory of spaces by Friedhelm Waldhausen.

answered Feb 5 2011 at 14:59

K.J. Moi

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Thomas Riepe · Answer 3 · 2011-02-05 09:39:00Z UTC

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I'd say, of course Quillen's "Higher algebraic K-theory I", the "K-theory Handbook".

answered Feb 5 2011 at 9:39

Thomas Riepe

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“Must read” papers in algebraic K-theory?

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