Timeline for Usefulness of using TQFTs
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Apr 4, 2011 at 23:21 | comment | added | Daniel Moskovich | @Jose: Fair enough- I exaggerated in order to emphasize a point. Undoubtedly, it was indeed Witten's paper which sparked the subject. I struck the passage out. | |
| Apr 4, 2011 at 23:19 | history | edited | Daniel Moskovich | CC BY-SA 2.5 |
added 17 characters in body; added 45 characters in body
|
| Apr 4, 2011 at 22:49 | comment | added | José Figueroa-O'Farrill | There seems to be some historical revisionism going on here. It is true that Schwarz (and independently also Singer, albeit unpublished) discovered a three-dimensional abelian Chern-Simons (aka BF) theory which computes the analytic Ray-Singer torsion of a 3-manifold. To further claim that this sparked the subject, though, seems to fly in the face of the evidence, not to mention the well-documented historical accounts by Atiyah, say. Whereas or not the work of Witten was motivated by Schwarz's BF theory is debatable, but that it was Witten's paper that sparked the subject is not. | |
| Apr 4, 2011 at 16:49 | comment | added | Charlie Frohman | Stepping away from $3$-manifolds, the highest impact of the ideas of TQFT came in combinatorial algebraic geometry. The Gromov-Witten potential allowed the solution of classical problems in enumerative geometry...that were not going to be solved by purely homotopy theoretic means. | |
| Apr 4, 2011 at 16:43 | comment | added | Charlie Frohman | ..and peripheral structure if the manifold has boundary. The TQFT underlying the Witten-Reshitkhin-Turaev invariant keeps track of peripheral structure also. You might try: Frohman, Charles; Kania-Bartoszyńska, Joanna A quantum obstruction to embedding. Math. Proc. Cambridge Philos. Soc. 131 (2001), no. 2, 279–293 and Frohman, Charles; Gelca, Răzvan; Lofaro, Walter The A-polynomial from the noncommutative viewpoint. Trans. Amer. Math. Soc. 354 (2002), no. 2, 735–747 for examples of using TQFT to construct invariants that detect peripheral structure. | |
| Apr 4, 2011 at 15:11 | history | edited | Daniel Moskovich | CC BY-SA 2.5 |
reference added
|
| Apr 4, 2011 at 14:58 | history | answered | Daniel Moskovich | CC BY-SA 2.5 |