Timeline for What's the current state of the classification of not-fully-extended TQFTs?
Current License: CC BY-SA 2.5
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| Jul 18, 2010 at 23:45 | comment | added | Kevin Walker | Maybe I shouldn't have said "characterize mapping class groups" in the original answer. The Hatcher-Thurston 2-complex was used to derive a presentation of the MCG, but for the TQFT application you need the 2-complex, not the presentation of the MCG. | |
| Jul 18, 2010 at 23:43 | comment | added | Kevin Walker | Sure. Hatcher and Thurston constructed a simply connected 2-complex for a surface Y, with vertices the pants decompositions of Y, edges "F" and "S" moves between pants decompositions, and some 2-cells (see math.cornell.edu/~hatcher/Papers/pantsdecomp.pdf). The Moore-Seiberg equations correspond to the Hatcher-Thurston 2-cells, or rather to lifts of those 2-cells to a similar 2-complex for pants decompositions "with seams". By "Hatcher-Thurston for 3-manifolds" I meant doing this when Y is a 3-manifold, maybe with vertices corresponding to compression-body decomps of Y. | |
| Jul 18, 2010 at 22:19 | comment | added | Ian Agol | hey Kevin, Can you expand upon what you mean by your last sentence (Hatcher-Thurston for 3-manifolds)? | |
| Jul 11, 2010 at 2:06 | vote | accept | Theo Johnson-Freyd | ||
| Jul 9, 2010 at 13:14 | history | answered | Kevin Walker | CC BY-SA 2.5 |