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Distance two links
Journal article   Peer reviewed

Distance two links

Ryan Blair, Marion Campisi, Jesse Johnson, Scott Taylor and Maggy Tomova
Geometriae Dedicata, Vol.180(1), pp.17-37
02/2016
DOI: 10.1007/s10711-015-0088-2

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Abstract

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 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. L is obtained by banding from another link $$L'$$ L ′ that has a bridge sphere of the same Euler characteristic as the bridge sphere for L but of distance 0 or 1.
Geometry Mathematics Links Distance in the curve complex Essential surfaces

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