18
$\begingroup$

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)

Improve this question
$\endgroup$
4
  • 2
    $\begingroup$ 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. $\endgroup$
    – Harry Gindi
    Commented Feb 5, 2011 at 12:58
  • $\begingroup$ 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. $\endgroup$
    – Harry Gindi
    Commented Feb 5, 2011 at 13:08
  • $\begingroup$ 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. $\endgroup$
    – Sean Tilson
    Commented Feb 6, 2011 at 4:58
  • 1
    $\begingroup$ @Harry: Lurie's course does not even mention K-theory. It is on L-theory; a completely different story. $\endgroup$
    – Johannes Ebert
    Commented Jul 23, 2012 at 9:44

5 Answers 5

Reset to default
16
$\begingroup$

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

Improve this answer
$\endgroup$
15
$\begingroup$

Algebraic K-theory of spaces by Friedhelm Waldhausen.

Improve this answer
$\endgroup$
6
$\begingroup$

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.

Improve this answer
$\endgroup$
3
  • $\begingroup$ Steven, could you give a (more) complete reference? $\endgroup$
    – Ryan Budney
    Commented Jul 23, 2012 at 0:33
  • $\begingroup$ I see there's two, one you reviewed on MathSciNet and one reviewed by Weibel. $\endgroup$
    – Ryan Budney
    Commented Jul 23, 2012 at 0:37
  • 4
    $\begingroup$ 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. $\endgroup$
    – Steven Landsburg
    Commented Jul 23, 2012 at 1:57
3
$\begingroup$

Quillen's "Higher Algebraic K-Theory I" is probably the best source for understanding the basics and the original intuition.

Thomason/Trobaugh is also an excellent paper, but it is a fairly large paper and very fundamental (so the first half of the paper is dedicated to construction of the basic objects).

And if you want a deeper understanding, you could have a look at some of Thomason's older papers, as well as some of Waldhausen's papers.

When I was learning Algebraic K-Theory, I kind of found it easier to understand by going backwards (i.e. I would think of something to get a kind of big picture, ask myself questions about why something might be true, and use that approach to go backwards through Thomason/Trobaugh and if necessary back to older papers). Not everyone will agree with this approach, but I felt that it helped me to build the intuition needed to progress in the subject.

Improve this answer
$\endgroup$
3
$\begingroup$

On the Lichtenbaum-Quillen Conjectures from a Stable Homotopy-Theoretic Viewpoint by Stephen A. Mitchell (around 60 pages) contains unbelievable amount of the very key information on both algebraic K-theory, stable homotopy theory, and their most exciting interactions. When I started reading it, I thought I knew some of both, and was overwhelmed by the breathtaking panorama the author was skillfully presenting, showing only the very essence and at the same time managing to convey deepness and importance of several highly technical methods. Fantastic paper!

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .