Multiple Bridge Surfaces Restrict Knot Distance
نویسنده
چکیده
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 − χ(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
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