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Given a hyperbolic knot, we prove that the Reidemeister torsion of any lift of the holonomy to SL(2,C) is invariant under mutation along a Conway sphere.
Whitehead torsion
J. Milnor · 1966
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Algebraic geometry
Robin Hartshorne · 1977
Earlier work this paper cites.
Degeneration and Regeneration of Geometric Structures on Three-Manifolds, 1986
Craig D. Hodgson · 1986
Earlier work this paper cites.
Reidemeister torsion in knot theory
V. G. Turaev · 1986
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Mutation and volumes of knots in
Daniel Ruberman · 1987
Earlier work this paper cites.
Representation theory
William Fulton and Joe Harris · 1991
Earlier work this paper cites.
Twisted Alexander polynomial for finitely presentable groups
Masaaki Wada · 1994
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Remarks on the
D. Cooper and D. D. Long · 1996
Cited alongside, same era.
Le théorème d’hyperbolisation pour les variétés fibrées de dimension 3
Jean-Pierre Otal · 1996
Cited alongside, same era.
The classification of nonsimple algebraic tangles
Ying-Qing Wu · 1996
Cited alongside, same era.
Torsion de Reidemeister pour les variétés hyperboliques
Joan Porti · 1997
Cited alongside, same era.
Thurston’s hyperbolization of Haken manifolds
Jean-Pierre Otal · 1998
Cited alongside, same era.
Twisted cohomology for hyperbolic three manifolds
Pere Menal-Ferrer and Joan Porti
Cited in the paper.
Character Varieties
Adam S. Sikora
Cited in the paper.
The Geometry and Topology of Three-Manifolds
William P. Thurston
Cited in the paper.
Mutations of links in genus
D. Cooper and W. B. R. Lickorish · 1999
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Computing arithmetic invariants of 3-manifolds
David Coulson, Oliver A. Goodman, Craig D. Hodgson, and Walter D. Neumann · 2000
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Character varieties of mutative 3-manifolds
Stephan Tillmann · 2004
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Invariants of genus 2 mutants
H. R. Morton and N. Ryder · 2009
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Behavior of knot invariants under genus 2 mutation
Nathan M. Dunfield, Stavros Garoufalidis, Alexander Shumakovitch, and Morwen Thistlethwaite · 2010
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Twisted alexander polynomials of hyperbolic knots
N. Dunfield, S. Friedl, and N. Jackson · 2011
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