geometry dash apk Damian Osajda (Wrocław) - Two-dimensional Artin groups and systolicity

Graphs, surfaces, and cube complexes
9 July 2018

Abstract: The talk is based on a joint work with Jingyin Huang (MPIM Bonn). 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.

geometry dash apk Damian Osajda (Wrocław) - Two-dimensional Artin groups and systolicity
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