Systolic complexes and group presentations

  • Mireille Soergel

    Université de Bourgogne, Dijon, France
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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.

Cite this article

Mireille Soergel, Systolic complexes and group presentations. Groups Geom. Dyn. 17 (2023), no. 3, pp. 899–921

DOI 10.4171/GGD/717