%0 Journal Article
%T Three-manifolds, virtual homology, and group determinants
%A Daryl Cooper
%A Genevieve S Walsh
%J Mathematics
%D 2006
%I arXiv
%R 10.2140/gt.2006.10.2247
%X We 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.
%U http://arxiv.org/abs/math/0603152v3