2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221824We apply representation theory to study the homology of equivariant Dehn-fillings of a given finite, regular cover of a compact 3-manifold with boundary a torus. This yields a polynomial which gives the rank of the part of the homology carried by the solid tori used for Dehn-filling. The polynomial is a symmetrized form of the group determinant studied by Frobenius and Dedekind. As a corollary every such hyperbolic 3-manifold has infinitely many virtually Haken Dehn-fillings.This is the version published by Geometry & Topology on 29 November 2006Geometric TopologyRepresentation Theory57M10, 20C10, 57M25text