CAT(0) and acylindrical-hyperbolicity conjectures for Artin groups
CAT(0) and acylindrical-hyperbolicity conjectures for Artin groups
Let be a finite simplicial graph, let be its Artin group, and write for its centre. A group is CAT(0) here if it acts properly and cocompactly on a CAT(0) space.
Artin groups' geometric conjectures. For every Artin group : (1) is CAT(0); and (2) the central quotient is acylindrically hyperbolic.
These questions are known for right-angled Artin groups, some classes of two-dimensional Artin groups, spherical Artin groups of rank for the CAT(0) assertion, and spherical Artin groups for the acylindrical-hyperbolicity assertion. They remain open in general.
Sources & referencesView supporting material
Primary source
Nicolas Vaskou, “Acylindrical hyperbolicity for Artin groups of dimension 2”, arXiv:2007.16169 (2021).
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