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We show that the bridge distance of a knot determines a lower bound on the genera of essential surfaces and Heegaard surfaces in the manifolds that result from non-trivial Dehn surgeries on the knot. In particular, knots with high bridge distance do not admit non-trivial non-hyperbolic surgeries or non-trivial cosmetic surgeries. We further show that if a knot has bridge distance at least 3 then its...
In this paper, we characterize all links in $$S^3$$ S 3 with bridge number at least three that have a bridge sphere of distance two. We show that if a link L has a bridge sphere of distance at most two then it falls into at least one of three categories: The exterior of L contains an essential meridional sphere. L can be decomposed as a tangle product of a Montesinos...
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