Garside categories, periodic loops and cyclic sets
| dc.creator | Bessis, David | |
| dc.date | 2006-10-26 | |
| dc.date.accessioned | 2026-07-07T07:29:27Z | |
| dc.date.available | 2026-07-07T07:29:27Z | |
| dc.description | Garside groupoids, as recently introduced by Krammer, generalise Garside groups. A weak Garside group is a group that is equivalent as a category to a Garside groupoid. We show that any periodic loop in a Garside groupoid $\CG$ may be viewed as a Garside element for a certain Garside structure on another Garside groupoid $\CG_m$, which is equivalent as a category to $\CG$. As a consequence, the centraliser of a periodic element in a weak Garside group is a weak Garside group. Our main tool is the notion of divided Garside categories, an analog for Garside categories of Bökstedt-Hsiang-Madsen's subdivisions of Connes' cyclic category. This tool is used in our separate proof of the $K(π,1)$ property for complex reflection arrangements | |
| dc.description | 33 pages. First abridged version | |
| dc.identifier | https://arxiv.org/abs/math/0610778 | |
| dc.identifier | http://arxiv.org/abs/math/0610778 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/118114 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.title | Garside categories, periodic loops and cyclic sets | |
| dc.type | text |