Torsion-free groups acting geometrically on the product of two trees

Abstract: Given a group acting geometrically on product of two trees, we know that one visual boundary is the topological join of two Cantor sets. We prove that these groups are "boundary rigid": any CAT(0) space on which the group acts has visual boundary homeomorphic to such a join. Since there is no hyperbolicity going on here, one cannot expect that the natural equivariant quasi-isometry between an arbitrary CAT(0) space and the product of two trees to extend to any sort of map on boundaries, thus the proof requires new techniques. The proof uses work of Ricks on recognising product splittings from the Tits boundary as well as work of Guralnik and Swenson on general dynamics of a CAT(0) group on both the visual and Tits boundary.

This is (recent) joint work with Jankiewicz, Karrer, and Sathaye.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( paper | slides )

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Geometry and topology online

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