Bonn Topology Group - Abstracts

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Talk

July 3rd 2018
Damian Osajda (Uniwersytet Wrocławski, Poland): Two-dimensional Artin groups and systolicity

Abstract

We show that two-dimensional Artin groups act geometrically on metrically systolic complexes. The latter are simply connected flag simplicial complexes with links satisfying some non-positive-curvature-like condition. As corollaries we obtain new results on two-dimensional Artin groups and all their finitely presented subgroups: the Dehn function is quadratic, the Conjugacy Problem is solvable. Furthermore, metric systolicity is used by us for studying quasi-isometric rigidity of such groups. In the particular case of large-type Artin groups the results are strengthened - such groups are systolic. In that case we conclude many other new properties, e.g. biautomaticity, existence of an EZ-boundary.
The talk is based on a joint work with Jingyin Huang (MPIM Bonn).

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