Timeline for A cohomology theory for fusion categories
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 27, 2018 at 10:49 | comment | added | Manuel Bärenz | One detail that puzzles me in what sense $H^3(A)$ would even be a group. It would mean in particular that every fusion ring has a "trivial" fusion category realising it (which can't be true in general, I think). So $H^3(A)$ seems less like a group but more like affine spaces? | |
| Nov 13, 2017 at 11:29 | vote | accept | Manuel Bärenz | ||
| Nov 13, 2017 at 11:27 | comment | added | Manuel Bärenz | My point about Davydov-Yetter was just this: In the finite group case, and a field like $\mathbb{R}$ or $\mathbb{C}$, $H^3(G, k^*)$ is a 0-dimensional manifold. It classifies (up to outer automorphisms) fusion categories of $G$-graded vector spaces. Since the tangent space of $k^*$ is $k$, and Davydov-Yetter classifies deformations of the associator, I found it reasonable to identify $H^3(G,k)$ (for a given $\operatorname{Vec}_G^\omega$) with the tangent space of $H^3(G,k^*)$ (at $\omega$). Now I was hoping that this viewpoint could be generalised somehow. | |
| Nov 13, 2017 at 11:24 | comment | added | Manuel Bärenz | Thank you very much! Is there any reference to these "certain kinds of graphs"? I think I've never seen anything like this. | |
| Nov 12, 2017 at 20:31 | history | edited | Noah Snyder | CC BY-SA 3.0 |
added 39 characters in body
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| Nov 12, 2017 at 20:16 | history | answered | Noah Snyder | CC BY-SA 3.0 |