Exceptional and cosmetic surgeries on knots

Ryan Blair; Marion Campisi; Jesse Johnson; Scott A. Taylor; Maggy Tomova

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arXiv · 1209.0197

Exceptional and cosmetic surgeries on knots

Ryan Blair·Marion Campisi·Jesse Johnson·Scott A. Taylor·Maggy Tomova

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Abstract

We show that the distance of a link $K$ with respect to a bridge surface of any genus determines a lower bound on the genus 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 bridge number is bounded above by a function of Seifert genus, or indeed by the genus of (almost) any essential surface or Heegaard surface in the surgered manifold.

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Ryan Blair, Marion Campisi, Jesse Johnson, Scott A. Taylor, Maggy Tomova. 2012-09-02. Exceptional and cosmetic surgeries on knots. https://arxiv.org/abs/1209.0197

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