Knots with the Lens Space Surgery

Abstract

In this paper we construct an infinite family of hyperbolic (1, 1)–knots with two parameters, and show that some of them admit exceptional Dehn surgery such as lens space surgery, Seifert surgery, and toroidal surgery. Furthermore, we give simple examples of hyperbolic (1, 1)–knots which admit two toroidal surgeries at distance four such that both toroidal surgeries do not create Klein bottles.