2006/03/09 by Jim E. Hoste, Hoste, Jim E., Patrick D. Shanahan +1
Mathematics · #57M25 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #math.CO #math.GT #msc:57M25
paper · pdf · doi:10.48550/arxiv.math/0603206
16 pages, 6 figures
arxiv created 2006/03/09 · arxiv updated 2009/12/01
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.