Multiple bridge surfaces restrict knot distance

Maggy Tomova

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Multiple bridge surfaces restrict knot distance

Maggy Tomova

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Abstract

Suppose M is a closed irreducible orientable 3-manifold, K is a knot in M, P and Q are bridge surfaces for K and K is not removable with respect to Q. We show that either Q is equivalent to P or $d(K,P) \leq 2-χ(Q-K)$. If K is not a two bridge knot, then the result holds even if K is removable with respect to Q. As a corollary we show that if a knot in the 3-sphere has high distance with respect to some bridge sphere and low bridge number, then the knot has a unique minimal bridge position.

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Maggy Tomova. 2006-11-16. Multiple bridge surfaces restrict knot distance. https://arxiv.org/abs/math/0511139

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