We construct a CAT(0) group containing a finitely presented subgroup with infinitely many conjugacy classes of finiteorder elements. Unlike previous examples (which were based on right-angled Artin… (More)

We construct 2-dimensional CAT(-1) groups which contain free subgroups with arbitrary iterated exponential distortion, and with distortion higher than any iterated exponential.

We define a family of quasi-isometry invariants of groups called higher divergence functions, which measure isoperimetric properties “at infinity.” We give sharp upper and lower bounds on the… (More)

Let Γ be a finitely generated group with a given word metric. The asymptotic density of elements in Γ that have a particular property P is the limit, as r → ∞, of the proportion of elements in the… (More)

We investigate the quasi-isometry classification of the right-angled Coxeter groups WΓ which are 1-ended and have triangle-free defining graph Γ. We begin by characterising those WΓ which split over… (More)