Three-manifolds, virtual homology, and group determinants
Geometric Topology
2009-03-02 v3 Representation Theory
Abstract
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.
Keywords
Cite
@article{arxiv.math/0603152,
title = {Three-manifolds, virtual homology, and group determinants},
author = {Daryl Cooper and Genevieve S Walsh},
journal= {arXiv preprint arXiv:math/0603152},
year = {2009}
}
Comments
This is the version published by Geometry & Topology on 29 November 2006