Timeline for Analogue of cyclic homology for e_n-algebras?
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6 events
| when toggle format | what | by | license | comment | |
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| Apr 21, 2014 at 18:39 | answer | added | Brian Williams | timeline score: 3 | |
| Sep 20, 2013 at 12:21 | comment | added | Sean Tilson | I think I have definitely lied to you. See Covering Homology by Brun, Carlsson, and Dundas or higher topological cyclic homology by Carlsson, Douglas, and Dundas. These might answer your question. | |
| Sep 19, 2013 at 18:34 | comment | added | Sean Tilson | The thing you want to have an analogy with doesn't have anything to do with a commutative structure. In fact, there is an analog of cyclic homology for associative algebras, TC. This is pretty hard to compute. There is also an analog of HH that is specific to $E_n$ algebras, iterated THH. I don't know of anyone who has investigated cycltomic structures on iterated THH in a way that remembers that it is iterated. That might be interesting. | |
| Feb 19, 2013 at 0:31 | comment | added | Geoffroy Horel | You might want to look at this paper : arxiv.org/abs/1104.0181 by Jon Francis. He shows that Hochschild cohomology of an e_n algebra is the Lie algebra of some derived algebraic group. Of course this doesn't really answer the question. | |
| Feb 14, 2013 at 21:40 | comment | added | Craig Westerland | This is not a great answer, but you can try to take the factorization homology of the $e_n$-algebra over $S^n$ (perhaps you need to assume that the algebra is framed). Then, since $S^n$ has an action of $SO(n+1)$, you could take the homotopy orbits (or fixed points) of the result. When $n=1$, this returns the usual definition of cyclic homology (or negative cyclic homology). But it's not obvious that this can be expressed in the terms that you're asking for above. | |
| Feb 14, 2013 at 20:14 | history | asked | nikitamarkarian | CC BY-SA 3.0 |