Timeline for DW, state sum models, and fully extended TQFTs
Current License: CC BY-SA 4.0
11 events
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| Sep 23, 2021 at 14:27 | comment | added | Student | (Thrilled to see you back in MOF. Have been enjoying your work!) And thanks a lot for your clarification! I was hoping for a (quantum?) bundle-like description of DW in the quantum case, similar to what the case of finite group can provide.. But now I believe it is just an analogy, and one should treat the bundle description as something as a motivation. | |
| Sep 23, 2021 at 6:40 | comment | added | Manuel Bärenz | > According to Manuel Bärenz's edit on nLab, it can be realized as a generalized DW theory, based on quantum groups instead of finite groups. I should really have said "with a ribbon (= braided spherical) fusion category" rather than "quantum group" back then. | |
| Apr 20, 2020 at 19:28 | answer | added | Noah Snyder | timeline score: 9 | |
| Apr 20, 2020 at 17:42 | comment | added | Arun Debray | I tried to write up a partial answer to these questions, but as far as I know very few of them have any concrete answers where one can point to proofs in the literature, or even statements. For example, a proof that Crane-Yetter theories are fully extended would require an understanding of the $\mathrm{SO}_4$-action on a certain 4-category, which is difficult and still open. Many questions about fully extended TFT (e.g. 2.2) depend on the choice of target, but are nonetheless open for any reasonable target. | |
| Apr 20, 2020 at 14:52 | history | edited | Student | CC BY-SA 4.0 |
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| Apr 20, 2020 at 6:37 | comment | added | Joao Faria Martins | If you have a look e.g. at "Topological Higher Gauge Theory - from BF to BFCG theory F. Girelli, H. Pfeiffer, E. M. Popescu: " you can find discussion of why Yetter homotopy 2-type TQFT can be seen as a DW with a finite 2-group. arxiv.org/abs/0708.3051". The relation to Higher Gauge theory (hence considering 2-bundles) is also discussed there in an references. | |
| Apr 20, 2020 at 6:33 | comment | added | Joao Faria Martins | Continuing the previous comment. One gets CY by doing the construction over SU(2), and then passing to quantum SU(2) at a root of unity in order to obtain a finite sum. | |
| Apr 20, 2020 at 6:27 | comment | added | Joao Faria Martins | For Q1.1 I would recommend "An Introduction to Spin Foam Models of Quantum Gravity and BF Theory, by John C. Baez: . arxiv.org/abs/gr-qc/9905087. DW with trivial cocycle could be thought of as a BF-theory with a finite group, at least in the classical level. | |
| Apr 20, 2020 at 2:20 | history | edited | Student | CC BY-SA 4.0 |
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| Apr 20, 2020 at 2:09 | history | edited | Student | CC BY-SA 4.0 |
added a link supporting my idea
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| Apr 20, 2020 at 1:57 | history | asked | Student | CC BY-SA 4.0 |