|J. Alev, D. Hernandez, B. Keller, Th. Levasseur, et S. Morier-Genoud.
|Email des responsables :
|Jacques Alev <firstname.lastname@example.org>, David Hernandez <email@example.com>, Bernhard Keller <firstname.lastname@example.org>, Thierry Levasseur <Thierry.Levasseur@univ-brest.fr>, Sophie Morier-Genoud <email@example.com>
|Info sur https://researchseminars.org/seminar/paris-algebra-seminar
Le séminaire est prévu en présence à l'IHP et à distance. Pour les liens et mots de passe, merci de contacter l'un des organisateurs ou de souscrire à la liste de diffusion https://listes.math.cnrs.fr/wws/info/paris-algebra-seminar. L'information nécessaire sera envoyée par courrier électronique peu avant chaque exposé. Les notes et transparents sont disponibles ici.
Since March 23, 2020, the seminar has been taking place remotely. For the links and passwords, please contact one of the organizers or
subscribe to the mailing list at https://listes.math.cnrs.fr/wws/info/paris-algebra-seminar. The connexion information will be emailed shortly before each talk. Slides and notes are available here.
|Owen Garnier - Amiens,
|Homology of a category and the Dehornoy-Lafont order complex
|14:00 à 15:00
The work of Squier and Kobayashi proves that the homology of a monoid can be computed using a so called complete rewriting system, which acts as a convenient presentation of the monoid. Later, Dehornoy and Lafont noted that such a convenient presentation arises in particular when considering monoids satisfying combinatorial assumptions regarding existence of lcms. This gave rise to the so called Dehornoy-Lafont order complex, which was used to compute the homology of complex braid groups by Callegaro and Marin. After giving a quick summary of these works, I will present a generalization of this latter complex to the case of a category which again satisfies convenient combinatorial assumptions. Of course, as my "true" goal is to compute the homology of a group using some associated category, I will also give a link between the homology of a category, that of its enveloping groupoid, and that of a group which is equivalent to the said groupoid. Lastly, I will explain an application to the case of the complex braid group B31B31, which is studied through its associated Garside category, and which was not directly covered by previous approaches.
This talk will take place in hybrid mode at the Institut Henri Poincaré.