Essential tori obtained by surgery on a knot

Mario Eudave-Muñoz

Vol. 167 (1995), No. 1, 81–117

DOI: 10.2140/pjm.1995.167.81

Abstract

It is proved that if Dehn surgery on a strongly invertible knot, which is not a satellite knot yields a manifold containing an incompressible torus, then the slope of the surgery consists of a certain number of meridians and at most two longitudes. Furthermore, if the slope has two longitudes, then there is an incompressible torus which meets the surgered solid torus twice.

Mathematical Subject Classification 2000

Primary: 57M25

Milestones

Received: 20 June 1992

Revised: 6 December 1992

Published: 1 January 1995