Generalization of the Dehornoy-Lafont order complex to categories. Application to exceptional braid groups

Autor:	Garnier, Owen
Rok vydání:	2023
Předmět:	Mathematics - Group Theory Mathematics - Representation Theory Primary 20J06 18G35 Secondary 20F36 20F55
Zdroj:	Applied Categorical Structure 32 (2024)
Druh dokumentu:	Working Paper
DOI:	10.1007/s10485-023-09757-6
Popis:	The homology of a Garside monoid, thus of a Garside group, can be computed efficiently through the use of the order complex defined by Dehornoy and Lafont. We construct a categorical generalization of this complex and we give some computational techniques which are useful for reducing computing time. We then use this construction to complete results of Salvetti, Callegaro and Marin regarding the homology of exceptional complex braid groups. We most notably study the case of the Borchardt braid group $B(G_{31})$ through its associated Garside category. Comment: 25 pages. 8 Tables
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2302.10033 Zobrazit plný text záznamu View this record from Arxiv