Presented by:
Ian Leary
Date:
Wednesday 21st June 2017 - 09:00 to 10:00
Venue:
INI Seminar Room 1
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
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
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