Distance Two Links

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

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arXiv · 1309.3787

Distance Two Links

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

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Abstract

In this paper, we characterize all links in the 3-sphere with bridge number at least three that have a bridge sphere of distance two. We show that a link L has a bridge sphere of distance at most two then it falls into at least one of three categories: (1) The exterior of L contains an essential meridional sphere. (2) L can be decomposed as a tangle product of a Montesinos tangle with an essential tangle in a way that respects the bridge surface and either the Montesinos tangle is rational or the essential tangle contains an incompressible, boundary-incompressible annulus. (3) L is obtained by banding from another link L' that has a bridge sphere of the same Euler characteristic as the bridge sphere for L but of distance 0 or 1.

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Ryan Blair, Marion Campisi, Jesse Johnson, Scott A. Taylor, Maggy Tomova. 2013-09-15. Distance Two Links. https://arxiv.org/abs/1309.3787

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