Ishikawa--Shimokawa conjecture on finite boundary slopes

Let KK be a knot in S3S^3, and let bb be a finite boundary slope for KK.

Ishikawa--Shimokawa conjecture. Then

b2c(K).|b| \leq 2c(K).

This follows immediately from the boundary slope diameter conjecture because 00, the slope of a Seifert surface, is always among the boundary slopes. It is attributed in the paper to Ishikawa and Shimokawa; the supplied text does not indicate that it has been resolved.

Sources & referencesView supporting material

Primary source

Thomas W. Mattman, Gabriel Maybrun and Kristin Robinson, “Boundary slope diameter and crossing number of 2-bridge knots”, arXiv:math/0510496 (2007).

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