Knots yielding homeomorphic lens spaces by Dehn surgery

Toshio Saito and Masakazu Teragaito

Vol. 244 (2010), No. 1, 169–192

DOI: 10.2140/pjm.2010.244.169

Abstract

We show that there exist infinitely many pairs of distinct knots in the 3-sphere such that each pair can yield homeomorphic lens spaces by the same Dehn surgery. Moreover, each knot of the pair can be chosen to be a torus knot, a satellite knot or a hyperbolic knot, except that both cannot be satellite knots simultaneously. This exception is shown to be unavoidable by the classical theory of binary quadratic forms.

Keywords

Dehn surgery, lens space, knot, Fibonacci number, binary quadratic form

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 11B39, 11E16

Milestones

Received: 20 August 2008

Accepted: 28 April 2009

Published: 17 November 2009