Strict Inequality Between Tunnel Numbers of a Satellite Knot and Its High Distance Companion

Abstract

Let K′ be a satellite knot of a knot K. If K is a high distance knot, then the tunnel numbers t(K′) and t(K) satisfy t(K′) ≥ t(K) + 1. The authors also give an example showing that the inequality above is sharp.

Keywords

Tunnel number / Satellite knot / High distance knot / 57K10 / 57K20 / 57K32

References

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