Geometry, Topology and Dynamics Seminar
MurphyKate Montee
University of Chicago
Random groups at density $d<3/14$ act on CAT(0) cube complexes.
Abstract: For random groups in the Gromov density model at $d<3/14$, we construct walls in the Cayley complex $X$ which give rise to a non-trivial action by isometries on a CAT(0) cube complex. This extends results of Ollivier-Wise and Mackay-Przytycki at densities $d<1/5$ and $d<5/24$, respectively. We are able to overcome one of the main combinatorial challenges remaining from the work of Mackay-Przytycki, and we give a construction that plausibly works at any density $d<1/4$.
Monday October 21, 2019 at 3:00 PM in 636 SEO