Taut polynomials from finite quotients of fibered hyperbolic 3-manifold groups

Abstract

We prove that the finite quotients of a fibered hyperbolic 3-manifold group detect the taut polynomials of fibered faces of the Thurston norm balls, whenever the monodromy map is fully-punctured. Toward this, we develop a general framework for the profinite invariance of twisted multivariable Alexander polynomials. We also identify specific hyperbolic one-cusped 3-manifolds that are profinitely rigid, by a strategy using normalized dilatations and the veering census.