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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)

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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 '11 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 '11 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 '11 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 '12 at 9:44
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3 Answers

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

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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.

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Steven, could you give a (more) complete reference? –  Ryan Budney Jul 23 '12 at 0:33
    
I see there's two, one you reviewed on MathSciNet and one reviewed by Weibel. –  Ryan Budney Jul 23 '12 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 '12 at 1:57
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