Consider the mapping class group Modg,p of a surface Σg,p of genus g with p punctures, and a finite collection {f1, . . . , fk} of mapping classes, each of which is either a Dehn twist about a simple… (More)

We study the action of the mapping class group on the integral homology of finite covers of a topological surface. We use the homological representation of the mapping class to construct a faithful… (More)

We study two–generated subgroups x f , gy Homeo pIq such that x f 2, g2y is isomorphic to Thompson’s group F, and such that the supports of f and g form a chain of two intervals. We show that this… (More)

For every orientable surface of finite negative Euler characteristic, we find a rightangled Artin group of cohomological dimension two which does not embed into the associated mapping class group.… (More)

In this article we study the right-angled Artin subgroups of a given rightangled Artin group. Starting with a graph Γ, we produce a new graph through a purely combinatorial procedure, and call it the… (More)

We prove that for each sufficiently complicated orientable surface S , there exists an infinite image linear representation ρ of π1(S ) such that if γ ∈ π1(S ) is freely homotopic to a simple closed… (More)

We prove that an arbitrary right-angled Artin group G admits a quasi-isometric group embedding into a right-angled Artin group defined by the opposite graph of a tree. Consequently, G admits… (More)

We study the residual properties of geometric 3–manifold groups. In particular, we study conditions under which geometric 3–manifold groups are virtually residually p for a prime p, and conditions… (More)

In this article we study the space of leftand bi-invariant orderings on a torsion-free nilpotent group G. We will show that generally the set of such orderings is equipped with a faithful action of… (More)