16-18 October 2013
Université d'Angers
Europe/Paris timezone

Coherent presentations of Artin groups

18 Oct 2013, 14:15
45m
Amphi L005 (bâtiment L) (Université d'Angers)

Amphi L005 (bâtiment L)

Université d'Angers

Université d'Angers, 2 Boulevard Lavoisier, 49045 Angers cedex 01
Exposé de recherche sur invitation Topologie algébrique et applications

Speaker

Mr Philippe Malbos (Institut Camille Jordan, Université Claude Bernard Lyon 1)

Description

A coherent presentation of a monoid is an extension of a presentation of this monoid by a homotopy basis, making a natural cellular complex associated to the presentation contractible. In the case of Artin monoids, we show that the usual presentation defined by Artin, using braid relations, can be completed in a coherent presentation that we give in an explicit way. Since any Artin monoid embeds in its Artin group, the coherent presentation of the monoid gives a coherent presentation of the group. I will show that our procedure gives a new proof of a theorem of Deligne concerning the action of an Artin monoid on a category in terms of a presentation based on the Garside structure. This is a joint work with Stéphane Gaussent and Yves Guiraud.
Mots Clés / Keywords Artin groups, rewriting, actions on categories

Primary author

Mr Philippe Malbos (Institut Camille Jordan, Université Claude Bernard Lyon 1)

Presentation Materials