Boundary Slope Diameter and Crossing Number of 2-Bridge Knots
- Date: 09/19/2007
Thomas Mattman (California State University, Chico)
University of British Columbia
In joint work with Maybrun and Robinson, we prove that for 2-bridge knots, the diameter of the set of boundary slopes is twice the crossing number. We also show that 2-bridge knots with four or fewer boundary slopes have a boundary slope of genus two or less. After some topological preliminaries, the argument quickly becomes combinatorial and is based on comparing various continued fraction representations of the same fraction.
Algebraic Topology Seminar 2007