Timeline for Motivation for algebraic K-theory?
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 31 at 20:39 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Dec 25, 2011 at 12:47 | comment | added | Justin Noel | Since there is now a paper on this, I would like to add that one can read about the universal characterization of higher K-theory that Tyler is discussing here: arxiv.org/abs/1001.2282 | |
| Jul 16, 2011 at 9:50 | comment | added | Thomas Riepe | Goncalo Tabuada's description of this talk mentions "the first conceptual characterization of Quillen's higher K-theory since Quillen's foundational work". Does anyone know where one could read about that?: mpim-bonn.mpg.de/node/3501 | |
| Mar 16, 2010 at 3:40 | comment | added | Tyler Lawson | That's the Barrat-Priddy-Quillen theorem. See Barrat-Priddy, "On the homology of non-connected monoids and their associated groups", and others reference Quillen, "The group completion of a simplicial monoid", Appendix Q in Friedlander-Mazur's "Filtrations on the homology of algebraic varieties". Also see Segal, "Configuration-spaces and iterated loop-spaces" for another take. | |
| Mar 15, 2010 at 21:21 | comment | added | roger123 | Nice to read! "The K-theory of the category of finite sets captures stable homotopy groups of spheres." I often heard this but never seen a precise statement and a proof. Can anybody provide me a reference? | |
| Nov 25, 2009 at 3:26 | comment | added | Mariano Suárez-Álvarez | It is universal in a specific sense. See the thesis of Gonçalo Tabuada. | |
| Nov 18, 2009 at 13:30 | comment | added | Tyler Lawson | I wasn't talking specifically about Quillen's higher K-theory functor, but about something homotopy equivalent, which produces a universal functor from symmetric monoidal categories to spectra that converts the symmetric monoidal structure into addition. | |
| Nov 18, 2009 at 9:10 | comment | added | Shizhuo Zhang | You mean Quillen Higher K-functor is universal? I doubt it very much, because Quillen never proved that. In fact, A.Rosenberg developed its a derived approach K theory which is universal and enjoy all the property of Quillen higher K-functor,moreover, it is universal. | |
| Oct 15, 2009 at 1:46 | vote | accept | S. Carnahan♦ | ||
| Oct 15, 2009 at 1:43 | history | answered | Tyler Lawson | CC BY-SA 2.5 |