Geodesic
Systolic complexes and group presentations
Mireille Soergel1 orcid
1Université de Bourgogne, Dijon, France
Groups, geometry, and dynamics, Tome 17 (2023) no. 3, pp. 899-921

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DOI

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.
DOI : 10.4171/ggd/717
Classification : 20-XX
Mots-clés : Systolic complexes, simplicial non-positive curvature, Garside groups

Mireille Soergel  1

1 Université de Bourgogne, Dijon, France 
Mireille Soergel. Systolic complexes and group presentations. Groups, geometry, and dynamics, Tome 17 (2023) no. 3, pp. 899-921. doi: 10.4171/ggd/717
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