Timeline for Explicit 3-cocycle of a cyclic group
Current License: CC BY-SA 3.0
6 events
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| Feb 8, 2014 at 18:38 | comment | added | wonderich | Plug it into n-cocycle conditions, you will know it is right. Each of $p_I$ are independent, not equivalent via n-coboundary conditions, so each of $p_I$ are distinct. It will be nice Andre may post an answer how mathematician derives this. (I have some TQFT intuition to derive it.) many thanks. | |
| Feb 8, 2014 at 8:47 | comment | added | André Henriques | Well... your reply still doesn't give me a way to independently check that your formula is correct. | |
| Feb 8, 2014 at 6:01 | comment | added | wonderich | To understand the cocycles, my method is by using the relation between Chern-Simons theory (partition function or path integral $Z$)and cohomology group('s cocycles): this 3-cocycle term actually shows us the so-called 2+1 dimensional Abelian Chern-Simons theory at the level $p_I$, which has a partition function: $Z=\int [DA]\exp[i\; p_{I} \int A \wedge d A]$, where A is 1-connection of a gauge group U(1) (or $\mathbb{Z}_n$ subgroup). I hope this physics field theory intuition helps. (p.s. I am a physicist.) | |
| Feb 8, 2014 at 5:21 | comment | added | André Henriques | Idear: The formula is indeed not too complicated. But I'd like to not just see it, but to also understand it. How did you find it? What makes you believe that it represents non-trivial elements of $H^3$? | |
| Feb 8, 2014 at 3:47 | history | edited | wonderich | CC BY-SA 3.0 |
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| Feb 8, 2014 at 0:10 | history | answered | wonderich | CC BY-SA 3.0 |