2017/10/14 by Jingyin Huang, Huang, Jingyin, Damian Osajda +1
Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.GR
paper · pdf · doi:10.48550/arxiv.1710.05157
final preprint version, to appear in Math. Ann
openalex publication_date 2017/10/14 · arxiv created 2019/03/15 · arxiv updated 2019/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the notion of metrically systolic simplicial complexes. We study geometric and large-scale properties of such complexes and of groups acting on them geometrically. We show that all two-dimensional Artin groups act geometrically on metrically systolic complexes. As direct corollaries we obtain new results on two-dimensional Artin groups and all their finitely presented subgroups: we prove that the Conjugacy Problem is solvable, and that the Dehn function is quadratic. We also show several large-scale features of finitely presented subgroups of two-dimensional Artin groups, lying background for further studies concerning their quasi-isometric rigidity.