Timeline for Uniqueness of Witten-Dijkgraaf 2D TQFT at 0th dimension
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 16, 2019 at 15:51 | comment | added | Student | No worries! I will dig into that. Thank you very much! | |
| Oct 15, 2019 at 21:33 | comment | added | Daniel Barter | Sorry, Vec(G) is the category of G-graded vector spaces. And yes, my claim is that if C and D are Morita equivalent fusion categories, then the corresponding Turaev-Viro TQFTs are equivalent. Unfortunately, I don't have a good reference. It is probably hidden somewhere in one of Kevin Walker's papers though. It is much easier to justify if you think about TQFT from a physicists perspective | |
| Oct 15, 2019 at 20:19 | comment | added | Student | What do you mean by Vec($G$) here? And what is true? Do you mean that "yes, the uniqueness is true up to 2-Morita equivalence"? Would you mind pointing out some reference for this? Thank you :) | |
| Oct 15, 2019 at 18:25 | comment | added | Daniel Barter | Yes, this is true. For example, Rep(G) and Vec(G) define the same TQFT. If two categories are 2-Morita equivalent, they have the same associated TQFTs | |
| Oct 15, 2019 at 2:53 | comment | added | Student | @DanielBarter The fact that the whole theory can be computed from the value of the point does not seem go guarantees uniqueness -- perhaps we can assign another category to $pt_+$ that still gives the same assignments to dimension $1$ and $2$ spaces. | |
| Oct 14, 2019 at 23:30 | comment | added | Daniel Barter | 3. Dikkgraaf-Witten theory is fully extended in all dimensions, so the answer is yes | |
| Oct 14, 2019 at 23:29 | comment | added | Daniel Barter | 1. The extension should definitely be unique because the whole theory can be computed from the value of the point. | |
| Oct 14, 2019 at 20:56 | history | asked | Student | CC BY-SA 4.0 |