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.
Citation
Daryl Cooper. Genevieve S Walsh. "Three-manifolds, virtual homology, and group determinants." Geom. Topol. 10 (4) 2247 - 2269, 2006. https://doi.org/10.2140/gt.2006.10.2247
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