Exceptional surgeries on certain $(1,1)$-knots

Abstract

We determine certain exceptional surgeries on a 3-parametric family of hyperbolic 1-bridge genus one knots ($(1,1)$-knots, in short). In particular, we show that such knots admit two infinite series of lens space surgeries. Our work is related to a nice paper of Teragaito [16], since we represent his toroidal manifolds as 2-fold coverings of the 3-sphere branched over well-specified links.