On Rank and Heegaard genus of 3-manifolds
by
Amelia C. Jones
Vassar College

We investigate a question of Waldhausen, which asks if the rank of the fundamental group of a 3-manifold differs from its Heegaard genus. Boileau and Zieschang produced examples of closed Seifert-fibred manifolds for which the Heegaard genus exceeds rank. It is still unknown if these two quantities ever differ for non-Seifert manifolds or bounded manifolds. For bounded manifolds, there is a sharper form of this question, the meridional generator conjecture. This conjecture asserts that meridional generators of the group correspond to bridges as properly interpreted. New results concerning knots and this conjecture will be presented.

Date received: February 1, 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-59.