Saddle tangencies and the distance of Heegaard splittings
Geometric Topology
2014-10-01 v2
Abstract
We give another proof of a theorem of Scharlemann and Tomova and of a theorem of Hartshorn. The two theorems together say the following. Let M be a compact orientable irreducible 3--manifold and P a Heegaard surface of M. Suppose Q is either an incompressible surface or a strongly irreducible Heegaard surface in M. Then either the Hempel distance d(P) <= 2 genus(Q) or P is isotopic to Q. This theorem can be naturally extended to bicompressible but weakly incompressible surfaces.
Keywords
Cite
@article{arxiv.math/0701396,
title = {Saddle tangencies and the distance of Heegaard splittings},
author = {Tao Li},
journal= {arXiv preprint arXiv:math/0701396},
year = {2014}
}