Coarse coherence of metric spaces and groups

Monday, August 1, 2022 - 2:00pm - 2:45pm
Keller 3-180
Boris Goldfarb (State University of New York - Albany)
I will introduce properties of metric spaces and, specifically, finitely generated groups with word metrics which are called “coarse coherence” and “coarse regular coherence”. They are geometric counterparts of the classical notion of coherence in homological algebra and the regular coherence property of groups defined and studied by Waldhausen. The properties make sense in the general context of coarse metric geometry and are coarse invariants of spaces and groups. They are in fact a weakening of Waldhausen's regular coherence. In a joint project with Gunnar Carlsson we show they can be used as effectively in K-theory computations. The family of all coarsely regular coherent groups is a very large class of groups containing all groups with straight finite decomposition complexity. This includes almost all known fundamental groups of aspherical manifolds. The new framework allows to prove structural results for the family by developing permanence properties of coarse coherence, a joint work with Jonathan Grossman.