Timeline for Mednykh's formula for 2d manifold with boundaries? How to count principal G-bundles with prescribed holonomies?
Current License: CC BY-SA 4.0
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| Nov 9, 2023 at 22:06 | history | edited | Sam Gunningham | CC BY-SA 4.0 |
Fixed what appeared to be a typo/sign error in the original (replaced 2g-2 2ith 2-2g).
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| Sep 17, 2020 at 10:26 | comment | added | Sam Gunningham | I personally haven't thought these kind of formulas for defects other than the ones where you label a boundary circle with a conjugacy class. | |
| Sep 17, 2020 at 10:26 | comment | added | Sam Gunningham | @Jordan There should be a Proposition 2.13 on page 18 of the paper. It basically gives the formula for the linear map associated to a punctured surface in terms of the orthogonal idempotents. | |
| Sep 15, 2020 at 19:36 | comment | added | Jordan | I am not sure if I should ask this as a separate question, but I was also wondering the following. The partition function of (untwisted) Dijkgraaf Witten theory for a finite group G just counts the number of principal bundles up to gauge transformations. However, when we have DW theory with defects, how do we count principal bundles with prescribed boundaries and defects?In arxiv.org/abs/1507.00941, they proposed a topological invariant for the case of defects but they are missing a representation theory formula that generalizes the ones above. Is it somewhere in the literature? | |
| Sep 15, 2020 at 19:00 | comment | added | Jordan | Thank you for your answer. Actually my question exactly came from studying 2d TQFT. However, I couldn't find Proportion 2.13 in your nice paper. Do you maybe mean Theorem 1.4, which has a similar expression for the symmetric group? | |
| Sep 15, 2020 at 18:48 | vote | accept | Jordan | ||
| Sep 15, 2020 at 10:37 | history | answered | Sam Gunningham | CC BY-SA 4.0 |