Computing Genera of Satellite Tunnel Number One Knots and Torti-rational Knots


We develop a method to compute the genera and slopes of essential surfaces in 2-bridge link exteriors with one longitudinal boundary component. The tools we use are those developed by Floyd and Hatcher in [1]. Such computations allow us to compute the genera of satellite tunnel number one knots and torti-rational knots.

[1] W. Floyd and A. Hatcher. The space of incompressible surfaces in a 2-bridge link complement. Trans. Amer. Math. Soc., 305(2):575–599, 1988

Osaka Journal