Metric-minimizing surfaces revisited

Petrunin, Anton; Stadler, Stephan

doi:10.2140/gt.2019.23.3111

Cited by 17 publications

(30 citation statements)

References 27 publications

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“…This naturally arises by examining the geometry of 2-dimensional Artin groups. It is interesting to compare this with the work of Petrunin and Stadler [PS17], where (roughly speaking) they showed any minimal disc in a CAT (0) space is CAT (0). Thus it is natural to wonder whether one can set up this weaker notion in a more analytical way and apply it to natural classes of examples.…”

Section: Introductionmentioning

confidence: 74%

Metric systolicity and two-dimensional Artin groups

Huang

Osajda

2019

Math. Ann.

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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 twodimensional 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.

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Section: Introductionmentioning

confidence: 74%