We generalize the JSJ-splitting of Rips and Sela to give decompositions of nitely presented groups which capture splittings over certain classes of small subgroups. Such classes include the class of… (More)

This paper addresses questions of quasi-isometric rigidity and classification for fundamental groups of finite graphs of groups, under the assumption that the BassSerre tree of the graph of groups… (More)

We combine ideas of Scott and Swarup on good position for almost invariant subsets of a group with ideas of Sageev on constructing cubings from such sets. We construct cubings which are more… (More)

Given a bounded valence, bushy tree T , we prove that any cobounded quasi-action of a group G on T is quasiconjugate to an action of G on another bounded valence, bushy tree T ′. This theorem has… (More)

We study atomic right-angled Artin groups – those whose defining graph has no cycles of length ≤ 4, and no separating vertices, separating edges, or separating vertex stars. We show that these groups… (More)

Given a bounded valence, bushy tree T , we prove that any cobounded quasi-action of a group G on T is quasiconjugate to an action of G on another bounded valence, bushy tree T . This theorem has many… (More)

We prove a Tits alternative theorem for groups acting on CAT(0) cubical complexes. Namely, suppose that G is a group for which there is a bound on the orders of its finite subgroups. We prove that if… (More)

We characterize the “best” model geometries for the class of virtually free groups, and we show that there is a countable infinity of distinct “best” model geometries in an appropriate sense–these… (More)