The Singer conjecture for hyperbolic 3-pseudomanifolds
Abstract:
In this talk, an aspherical 3-pseudomanifold is an aspherical 3-manifold with cone points, i.e., an aspherical cell complex in which every point has a neighborhood homeomorphic to a 3-ball, except for finitely many vertices that have neighborhoods homeomorphic to cones over closed surfaces of positive genus. Examples arise from right-angled Coxeter groups (RACGs) whose defining graph is a flag triangulation of a surface, or by coning off the boundary of a 3-manifold and applying a hyperbolization procedure.
We will discuss how to compute the L^2 homology for a large class of 3-pseudomanifolds, and prove a version of the Singer conjecture in this context. As an application, we verify a conjecture of Davis-Okun about the aforementioned family of RACGs, and we also obtain that these RACGs are virtually algebraically fibered and incoherent. This is joint work with G. Walsh.