Timeline for Chas-Sullivan string topology
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 1, 2010 at 17:38 | vote | accept | Kevin H. Lin | ||
| Mar 2, 2010 at 18:48 | answer | added | Matthias Kreck | timeline score: 11 | |
| Mar 2, 2010 at 18:19 | comment | added | Kevin H. Lin | Andrew: I am not dismissive of homotopy theory at all, nor do I dislike homotopy theory. It was definitely not my intention to sound that way. I just wanted to know if the arguments of Chas-Sullivan could be made rigorous. | |
| Mar 2, 2010 at 8:42 | comment | added | Andrew Stacey | @Tim: That wasn't my point. I was reacting to the slightly dismissive tone of "via homotopy theoretic methods" and "without using any homotopy theory". Transversality arguments need homotopy theory! It seemed that the question was "I don't like homotopy theory, can string topology be done geometrically?" and I wished to point out that the "homotopy theory" method of Cohen and Jones is actually very geometric and "hands on". There's no "up to homotopy" in the actual construction. | |
| Mar 1, 2010 at 21:40 | comment | added | Tim Perutz | @Andrew. Intersection theory on ordinary manifolds can be understood cohomologically (etc. etc.), but that doesn't vitiate the usefulness of transversality theory. A rigorous version of Chas-Sullivan might help validate, e.g., Fukaya's observation that the fundamental chain for the moduli space of least-area pseudo-holomorphic discs in a symp manifold with Lagrangian b.c. should satisfy the Maurer-Cartan equation with respect to the string bracket in the Lagrangian. | |
| Mar 1, 2010 at 21:13 | comment | added | Kevin H. Lin | I don't have any problems with it. I am just wondering whether it's possible to make the original idea rigorous, that's all. | |
| Mar 1, 2010 at 20:49 | comment | added | Andrew Stacey | Could you explain exactly what you don't like about the Cohen-Jones set up? I've always thought it very constructive! It's all about loop spaces and explicit pull-back maps. I know it works in cohomology rather than homology, is that your issue? Incidentally, you should also look up work by Veronique Godin on this. | |
| Mar 1, 2010 at 20:49 | answer | added | Don Stanley | timeline score: 7 | |
| Mar 1, 2010 at 20:30 | history | asked | Kevin H. Lin | CC BY-SA 2.5 |