7. Parabolic subgroups
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Problem 7.1.
Are intersections of parabolic subgroups themselves parabolic? More specifically: is this true in the Euclidean case? -
Problem 7.2.
Are intersections of parabolic again parabolic when the Deligne complex has some notion of non-positive curvature? (i.e., systolic, injective, CUB, \mathrm{CAT}(0)) -
Problem 7.3.
Let A be an Artin group with subgroup H. If for all h \in H there is a (spherical) parabolic containing h, does there exist a (spherical) parabolic containing H? Geometric version: If a group G acts on X and H < G with each h \in H fixing a point of X, then does H fix a point? What about when X has non-positive curvature?
Cite this as: AimPL: Geometry and topology of Artin groups, available at http://aimpl.org/geomartingp.