Pallavi Dani

Divergence in right-angled Coxeter groups

Let W be a 2-dimensional right-angled Coxeter group. We characterise such W with linear and quadratic divergence, and construct right-angled Coxeter groups with divergence poly- nomial of arbitrary degree. Our proofs use the structure of walls in the Davis complex.

Homological and homotopical Dehn functions are different

The homological and homotopical Dehn functions are different ways of measuring the difficulty of filling a closed curve inside a group or a space. The homological Dehn function measures fillings of cycles by chains, whereas the homotopical Dehn function measures fillings of curves by disks. Because the two definitions involve different sorts of boundaries and fillings, there is no a priori relationship between the two functions; however, before this work, there were no known examples of finitely presented groups for which the two functions differ. This paper gives such examples, constructed by amalgamating a free-by-cyclic group with several Bestvina–Brady groups.

Super-exponential 2-dimensional Dehn functions

We produce examples of groups of type F_3 with 2-dimensional Dehn functions of the form exp^n(x) (a tower of exponentials of height n), where n is any natural number.

Super-exponential distortion of subgroups of CAT(−1) groups

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