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Torsion polynomials connect the genus of a hyperbolic knot (a topological invariant) with the discrete faithful representation (a geometric invariant).
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Stavros Garoufalidis, Dylan Thurston, and Christian Zickert, The complex volume of SL ( n , ℂ ) {\rm SL}(n,\mathbb{C}) -representations of 3-manifolds , Duke Math. J. 164
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