4. Non-positive curvature
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Problem 4.15.
Prove that hyperbolic triangle Artin groups do not act properly on a \mathrm{CAT}(0) cube complex. -
Problem 4.2.
Does the \tilde{A}_2 Artin group act properly and cocompactly on a Helly graph? -
Problem 4.25.
Further classify the systolic Artin groups. -
Problem 4.35.
For a,b \in A, say a \leq b if there is a positive word c with a = bc. Is (A,\leq) a join-semilattice? -
Acylindrical hyperbolicity
Conjecture 4.4.
All non-spherical irreducible Artin groups are acylindrically hyperbolic. -
Problem 4.45.
Describe the hyperbolic space on which the acylindrically hyperbolic Artin groups act. -
Problem 4.5.
Is there a “largest” acylindrically hyperbolic space on which these Artin groups act that sees all loxodromic elements?
Cite this as: AimPL: Geometry and topology of Artin groups, available at http://aimpl.org/geomartingp.