Montesinos-versus-pretzel characterization of m-stair-step bridge spectra

Let M0M_0 be a Montesinos knot, and let K=cable(Tm,n,M0)K={\mathsf {cable}}(T_{m,n},M_0) be an (m,n)(m,n)-cable of M0M_0. The bridge spectrum of KK is the Montesinos–pretzel bridge-spectrum conjecture. mm-stair-step if and only if M0M_0 is not a pretzel knot. The conjecture is motivated by the absence of degeneration for 2-bridge knots and by the observed distinction between pretzel and non-pretzel Montesinos knots. The source says there is less direct evidence for this claim, so its status remains open.

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Primary source

Nicholas Owad, “Bridge spectra of cables of 2-bridge knots”, arXiv:1706.03653 (2017).

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