Boundary slopes of 2-bridge links determine the crossing number

Details Boundary slopes of 2-bridge links determine the crossing number Boundary slopes of 2-bridge links determine the crossing number

2006-03-09

arxiv.org/abs/math/0603206v1

Mathematics

Geometric Topology

16 pages, 6 figures

Scientific paper

A diagonal surface in a link exterior M is a properly embedded, incompressible, boundary incompressible surface which furthermore has the same number of boundary components and same slope on each component of the boundary of M. We derive a formula for the boundary slope of a diagonal surface in the exterior of a 2-bridge link which is analogous to the formula for the boundary slope of a 2-bridge knot found by Hatcher and Thurston. Using this formula we show that the diameter of a 2-bridge link, that is, the difference between the smallest and largest finite slopes of diagonal surfaces, is equal to the crossing number.

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