2023 - T2 - WS1 - GAP XVIII: Homotopy algebras and higher structures

Collection 2023 - T2 - WS1 - GAP XVIII: Homotopy algebras and higher structures

Organisateur(s) Cattaneo, Alberto ; Jotz, Madeleine ; Liao, Hsuan-Yi ; Schiavina, Michele ; Stiénon, Mathieu ; Xu, Ping

Date(s) 22/05/2023 - 26/05/2023

URL associée https://indico.math.cnrs.fr/event/7882/

11 16

Higher operations from algebra and geometry

De Ralph Kaufmann

Higher operations appear in the context of up to homotopy equations. For instance the pre-Lie product is a homotopy for the commutator. Such higher operations are often associated with a graphical or geometric calculus. In new work with Rivera and Wang, we find a natural Poisson double bracket as such a homotopy, which is a member of a series of even higher brackets. Interestingly the odd brackets vanish in a directed setting, but can be defined in an undirected setting. The double bracket yields a homotopy for a four term relation involving a product, a coproduct and their opposites. It dualizes to an $m_3$ multiplicaton which is part of an $A_∞$ structure with all $m_i > 4$ vanishing. Such structures were also studied in a different context by N. Iyudu, M. Kontsevich, and Y. Vlassopoulos.

Informations sur la vidéo

Date de captation 25/05/2023
Date de publication 25/05/2023
Institut IHP
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Alexandre Duplessis
Format MP4
Lieu IHP - Hermite Amphitheater

Domaine(s)

Topologie algébrique

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