Distance two links

作者：Blair Ryan^*; Campisi Marion; Johnson Jesse; Taylor Scott A; Tomova Maggy

来源：Geometriae Dedicata, 2016, 180(1): 17-37.

DOI：10.1007/s10711-015-0088-2

• Links
• Distance in the curve complex
• Essential surfaces

In this paper, we characterize all links in 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' that has a bridge sphere of the same Euler characteristic as the bridge sphere for L but of distance 0 or 1.

• 出版日期2016-2