Séminaires : Séminaire d'Algèbre

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.