Divergence in right-angled Coxeter groups


Anne Thomas


University of Sydney


Tue, 23/04/2019 - 12:00pm to 1:00pm


RC-4082, The Red Centre, UNSW


The notion of divergence of geodesics was introduced by Gromov in the 1980s as a way of quantifying how fast a pair of geodesic rays in a space move away from each other.  Gersten then used this idea to formulate a quasi-isometry invariant for groups, also called divergence.  We study divergence in right-angled Coxeter groups (RACGs), which are reflection groups such that each pair of generating reflections either commutes or generates an infinite dihedral group.  For certain such groups we characterise quadratic divergence, and for each positive integer d we exhibit a RACG with divergence polynomial of degree d.  This is joint work with Pallavi Dani.

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