Small Surfaces and Dehn Filling
by
Cameron Gordon
University of Texas

If M is a 3-manifold with a torus boundary component T, one can perform Dehn filling on M by attaching a solid torus to M along T, the resulting manifold M(r) being determined by the isotopy class r on T of a meridian of the solid torus. Now every 3-manifold can be decomposed into canonical pieces that are simple, i.e. contain no essential surfaces of non-negative euler characteristic (spheres, disks, tori or annuli), and one can ask: If M is simple, when is M(r) not simple? We will describe results on this question. In particular, the maximum possible values, for the intersection number between slopes r and s such that M(r) and M(s) contain essential surfaces of non-negative euler characteristic of a given pair of topological types, are now known, in all ten cases.

Date received: February 16, 1998

Copyright © 1998 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 # caas-86.