Triangulated 3-manifolds
by
Martin Scharlemann
University of California, Santa Barbara

In early attempts to classify manifolds, topologists studied and compared possible triangulations. They thereby succeeded in classifying 1- and 2-manifolds, but were eventually satisfied that this approach was not terribly useful for manifolds of dimension 4 and higher. For 3-manifolds, the use of triangulations (or Heegaard splittings as they're called in the trade) was at first promising, eventually disappointing, but has recently attracted attention again. Modern advances have given us a clearer picture of how Heegaard splittings behave and several new 3-manifold techniques have been based on their properties.

We'll discuss these new insights in general and, more specifically, new techniques for comparing Heegaard splittings of the same 3-manifold.

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-49.