Finite quotients of fibered, hyperbolic 3-manifold groups

The finite quotients of the fundamental group of a 3-manifold are the deck groups of its finite regular covers. We often pass to these finite-sheeted covers for different reasons, and these deck groups are organized into a topological group called the profinite completion of a 3-manifold group. In this talk, we will discuss how to leverage certain properties of mapping class groups of finite-type surfaces to study the profinite completions of the fundamental groups of fibered hyperbolic 3-manifolds of finite volume.