Timeline for Do all 3D TQFTs come from Reshetikhin-Turaev?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Aug 5, 2010 at 3:52 | comment | added | Anton Kapustin | Rozansky-Witten model for a compact hyperkahler target space (e.g. K3 surface) is an example of a non-semi-simple 3d TQFT. Z(S^1) is the 2-periodic derived category of coherent sheaves on the target. | |
| Oct 13, 2009 at 16:31 | comment | added | Chris Schommer-Pries | I took a look at this book, and it did seem to me that they form a sort of TQFT (with "exotic anomaly") out of non-semisimple MTCs. The anomaly they use is "exotic" (my word) and corresponds to a central extension of the bordism 2-category, not by a group but by a monoid (I think it was the natural numbers). This way they can get a weird TQFT where the value of, say, S<sup>1</sup> x S<sup>2</sup> is zero. (This can't happen in a usual TQFT without this anomaly since the value of S<sup>1</sup> x S<sup>2</sup> is the trace of the identity. ) | |
| Oct 13, 2009 at 14:33 | comment | added | Noah Snyder | You're probably right that that only works for closed things. What about the book "Non-semisimple topological quantum field theories for 3-manifolds with corners"? | |
| Oct 13, 2009 at 11:51 | comment | added | Kevin H. Lin | "there are known non-semisimple TQFTs" -- What's the definition of semisimple here? | |
| Oct 13, 2009 at 7:03 | comment | added | Kevin Walker | I thought Virelizier's stuff was just for closed 3-manifolds. I would be (happily) surprised if someone had worked out a non-semisimple example which gave a functor on 3-dimensional bordisms and was well-behaved axiomatically. | |
| Oct 13, 2009 at 6:03 | history | answered | Noah Snyder | CC BY-SA 2.5 |