Hyperbolic torsion polynomial conjecture for knot genus

Let KK be a hyperbolic knot in S3S^3, and let b[?25l\cTKb[?25h\C[t±1]b[?25l\cT_Kb[?25h \in \C[t^{\pm1}] be its hyperbolic torsion polynomial. The Seifert genus of KK is denoted by g(K)g(K). Hyperbolic torsion polynomial conjecture. The hyperbolic torsion polynomial determines the Seifert genus g(K)g(K); precisely,

deg\cTK=4g(K)2.\deg{\cT_K} = 4g(K)-2.

This conjecture proposes that the hyperbolic holonomy representation alone detects the genus of every hyperbolic knot in S3S^3, giving a sharp lower bound for the Thurston norm. It is motivated by experimental evidence and the results established for broad classes of hyperbolic knots, but its general status is not specified here.

Sources & referencesView supporting material

Primary source

Ian Agol and Nathan M. Dunfield, “Certifying the Thurston norm via SL(2, C)-twisted homology”, arXiv:1501.02136 (2015).

Additional references

2 papers in this index state this conjecture (2011–2015). The statement above is taken from the most recent of them; the others are arXiv:1108.3045.

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