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Journal Articles Groups, Geometry, and Dynamics Year : 2023

Systolic complexes and group presentations

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.

Dates and versions

hal-04356454 , version 1 (20-12-2023)

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Cite

Mireille Soergel. Systolic complexes and group presentations. Groups, Geometry, and Dynamics, 2023, 17 (3), pp.899-921. ⟨10.4171/GGD/717⟩. ⟨hal-04356454⟩
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