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Generalized Bestvina-Brady groups and their applications

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NPCW05 - Group actions and cohomology in non-positive curvature

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).

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