Multiple bridge surfaces restrict knot distance

By Maggy Tomova. 2005

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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 / 2 .Q K/ . If K is not a 2–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 S has high distance with respect to some bridge sphere and low bridge number, then the knot has a unique minimal bridge position.

Subfields: Geometry and Topology, Mathematical Physics, Neurology

View Paper: https://www.semanticscholar.org/paper/9080a13ad372c608790a9fbf8c2f92f8a70992db

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