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A calculation of the hyperbolic torsion polynomial of a pretzel knot. (English) Zbl 1423.57031
Summary: In this short note, we calculate the highest degree term of the hyperbolic torsion polynomial of a pretzel knot with three tangles. It gives a supporting evidence for a conjecture of Dunfield, Friedl and Jackson [N. M. Dunfield et al., Exp. Math. 21, No. 4, 329–352 (2012; Zbl 1266.57008)] that the hyperbolic torsion polynomial determines the genus and fiberedness of a hyperbolic knot.

57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
57M05 Fundamental group, presentations, free differential calculus
57M25 Knots and links in the \(3\)-sphere (MSC2010)
57Q45 Knots and links in high dimensions (PL-topology) (MSC2010)
Full Text: Euclid
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