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Three-manifolds, virtual
homology, and group determinants
Daryl Cooper and Genevieve S Walsh |
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Geometry & Topology 10 (2006) 2247–2269
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arXiv: math.GT/0603152 |
Abstract |
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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
Group determinant, Dehn-filling, virtually Haken
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Mathematical Subject Classification 2000
Primary: 57M10
Secondary: 57M25, 20C10
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References |
Forward citations |
Publication
Received: 8 March 2006
Accepted: 24 October 2006
Published: 29 November 2006
Proposed: David Gabai
Seconded: Cameron Gordon, Joan Birman
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Authors |
| Daryl Cooper | |
| Math Department UCSB Santa Barbara, CA 93106 USA |
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| Genevieve S Walsh | |
| Department of Math Tufts University Medford, MA 02155 USA and Département de Mathématiques UQAM Montréal, QC H3C 3J7 Canada |
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