Timeline for Do TQFTs give a complete set of invariants of manifolds?
Current License: CC BY-SA 3.0
10 events
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| Apr 27, 2018 at 10:58 | comment | added | Manuel Bärenz | @QiaochuYuan, is that so clear? Is isomorphism in the bordism category the same as in the category of smooth manifolds? | |
| Jan 14, 2018 at 19:24 | comment | added | Henry | @QiaochuYuan Yes, of course. I was assuming that the target is the category of vector spaces. Thanks for pointing it out. | |
| Jan 14, 2018 at 19:20 | comment | added | Henry | @skupers Thanks for the reference. I was intentionally vague, as I wanted to know the limitations of TQFTs in general (with a lot of different variants), not a specific version of it, in capturing some information of manifolds. But if I were to be more specific, I am most interested in the TQFTs as defined in the Atiyah's original paper: math.ru.nl/~mueger/TQFT/At.pdf. | |
| Jan 14, 2018 at 10:01 | comment | added | Qiaochu Yuan | If you allow TQFTs with arbitrary targets, then there is a universal one, namely the identity functor, which is a complete invariant tautologously. So some comstraints are needed on the target, e.g. that it be linear. | |
| S Jan 14, 2018 at 1:15 | history | edited | YCor |
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| S Jan 14, 2018 at 1:15 | history | suggested | Arun Debray |
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| Jan 14, 2018 at 0:30 | review | Suggested edits | |||
| S Jan 14, 2018 at 1:15 | |||||
| Jan 13, 2018 at 23:56 | comment | added | skupers | You're a bit vague about the exact field theories you're allowing. Can you give more details? But a certain variant does not distinguish smooth 4-manifolds: arxiv.org/abs/math/0503054. | |
| Jan 13, 2018 at 22:28 | review | First posts | |||
| Jan 13, 2018 at 22:49 | |||||
| Jan 13, 2018 at 22:26 | history | asked | Henry | CC BY-SA 3.0 |