Reducible Dehn surgery
by
Luis Gerardo Valdez-Sánchez
University of Texas at El Paso

Let M be a compact, orientable, irreducible 3-manifold with incompressible torus boundary. We show that if M' is a reducible Dehn-filling of M, then either M' is a connected sum of two lens spaces or M contains an essential torus T with or without boundary; in the later case the torus T dies after surgery.

In the particular case when M is a nontrivial knot exterior, this implies that the cabling conjecture holds for knots without essential tori with boundary in their exterior and with reducible surgery not a connected sum of two lens spaces. Relations with earlier work of C. Gordon and J. Luecke will be discussed.

We also prove that if M admits two reducible surgeries, one of which does not have lens space summands, then the prime factors of the other surgery are all, with at most one exception, t-manifolds. The case when M is a knot exterior will be treated separately.

Date received: February 18, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caak-53.