Nguyen Thanh Hoang (DaNang University of Education)

Title: Largest hyperbolic actions on 3-manifold groups

Abstract: A group will admit many different co-bounded actions on different hyperbolic spaces. Abbott-Osin-Baalasuramanya introduces a partial order on the set of all actions of a given group, where, roughly speaking, one action is larger than another if the smaller space can be formed by equivariantly collapsing some subspace of the larger. In some sense, the larger action in this partial order, the more information about the geometry of the group it should provide. The group is called H-accessible if the poset contains the largest element. In this talk, we show that the fundamental group of a nongeometric 3-manifold is not H-accessible.