2006/03/03 by Johnson, Jesse
#57M #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.math/0603102
We show that there are hyperbolic tunnel-number one knots with arbitrarily high bridge number and that "most" tunnel-number one knots are not one-bridge with respect to an unknotted torus. The proof relies on a connection between bridge number and a certain distance in the curve complex of a genus-two surface.