Radhika Gupta

Conformal dimension of the Bowditch boundary of certain Coxeter groups

Quasi-isometry (QI) classification of finitely generated groups is an important problem in geometric group theory. When two Gromov hyperbolic groups are quasi-isometric, then they have homeomorphic visual boundaries. But the converse is not true. One tool to distinguish two hyperbolic groups with the same visual boundary is to show that the conformal dimension, which is an analytic QI invariant, of the two boundaries are different. In this talk, we consider a particular family of Coxeter groups that are hyperbolic relative to free abelian subgroups (CAT(0) with isolated flats). We give the first computation of bounds for the conformal dimension of the Bowditch boundary of a non-hyperbolic group. As a corollary, we show that there are infinitely many QI classes of groups in this family of Coxeter groups (which all have the same visual boundary by the work of Haulmark-Hruska-Sathaye). In the process, we also construct a CAT(-1) geometry for non-hyperbolic Coxeter groups in our family. This is joint work with Elizabeth Field, Robbie Lyman and Emily Stark.