Systolic complexes and group presentations
Group Theory
2021-05-05 v1
Abstract
We give conditions on a presentation of a group, which imply that its Cayley complex is simplicial and the flag complex of the Cayley complex is systolic. We then apply this to Garside groups and Artin groups. We give a classification of the Garside groups whose presentation using the simple elements as generators satisfy our conditions. We then also give a dual presentation for Artin groups and identify in which cases the flag complex of the Cayley complex is systolic.
Keywords
Cite
@article{arxiv.2105.01345,
title = {Systolic complexes and group presentations},
author = {Mireille Soergel},
journal= {arXiv preprint arXiv:2105.01345},
year = {2021}
}