Abstract

Co-authors: Robert Kropholler (Tufts University), Ignat Soroko (University of Oklahoma)

In the 1990's Bestvina and Brady used Morse theory to exhibit (as subgroups of right-angled Artin groups) the first examples of groups that are but not finitely presented.

The speaker has generalized this construction, via branched coverings, to construct continuously many groups of type , including groups of type FP that do not embed in any finitely presented group.

I shall discuss the construction and some applications, including the theorem that every countable group embeds in a group of type and the construction of continuously many quasi-isometry classes of acyclic 4-manifolds admitting free, cocompact, properly discontinuous discrete group action (the latter joint with Robert Kropholler and Ignat Soroko).

Related Links

• https://arxiv.org/abs/1512.06609 – Archive link to preprint with main result
• https://arxiv.org/abs/1610.05813 – Archive link to preprint on subgroups of groups