Timeline for String cobracket and co-Hochschild homology
Current License: CC BY-SA 4.0
4 events
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| Sep 3 at 17:56 | comment | added | Manuel Rivera | Namely, instead of using a Frobenius algebra structure, in the non-simply connected case you may express Poincaré duality (capping with the fundamental class of $M$) as inducing a Calabi-Yau structure $A^! \simeq A$ for $A=C_*(\Omega M)$. This can be expressed entirely in the language of chains and comodules using that $A$ is quasi-isomorphic to the cobar construction on the singular chains $C_*(M)$. Then you plug $C_*(M)$ into the coHochschild complex to obtain a model for the free loop space and the use the appropriate version of duality on $C_*(M)$ to recover string topology. | |
| Sep 3 at 5:41 | comment | added | Qwert Otto | @ManuelRivera Thank you for the comment. I'll take a look at your preprint. | |
| Sep 2 at 1:43 | comment | added | Manuel Rivera | Hi, take a look at the introduction here: arxiv.org/abs/2308.09684. This is an explicit algebraic model for the coproduct in the non-simply connected case. This may be reformulated in terms of the coHochschild complex of an appropriate coalgebra model for M. In the non-simply connected setting, chain level Poincaré duality (with local coefficients) can formulated in the language of comodules using Koszul duality theory. The cobracket requires a bit of more work but it can be worked out as well. Send me an email if you have more questions! | |
| Sep 1 at 16:14 | history | asked | Qwert Otto | CC BY-SA 4.0 |