Bounding the number of boundary components of an essential surface in a knot exterior
by
John Luecke
University of Texas, Austin

We conjecture that there is a function, \tau, from the nonnegative integers to the nonnegative integers having the following property: If K is a knot in the 3-sphere which admits a Dehn surgery containing an essential surface of genus g then the exterior of K contains a properly embedded essential surface of genus at most g with at most \tau(g) boundary components. Note that \tau is independent of K. We prove the existence of \tau in the case where the surgery slope is non-integral.

Date received: January 31, 1996

Copyright © 1996 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 # caaa-37.