Three-manifolds, virtual homology, and group determinants

Details Three-manifolds, virtual homology, and group determinants Three-manifolds, virtual homology, and group determinants

2006-03-07

arxiv.org/abs/math/0603152v3

Geom. Topol. 10 (2006) 2247-2269

Mathematics

Geometric Topology

This is the version published by Geometry & Topology on 29 November 2006

Scientific paper

10.2140/gt.2006.10.2247

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.

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