Topology and Geometric Group Theory Seminar

Zachary MunroMcGill University
Lower bounds on cubical dimension of random groups

Thursday, March 16, 2023 - 2:45pm
Malott 206

Gromov defined a model of random groups with a density parameter d\in (0,1). Notably, Ollivier completed a proof of Gromov that at density d < 1/2 a random group is infinite, torsion-free, hyperbolic, with cohomological dimension 2. At density d > 1/2 a random group is either trivial or Z/2Z. Dahmani, Guirardel, and Przytycki proved that random groups do not split over finite subgroups. This is equivalent to saying random groups do not act with unbounded orbits on trees, i.e. one-dimensional CAT(0) cube complexes. We prove random groups do not act with unbounded orbits on CAT(0) square complexes.