Alternate Heegaard genus bounds distance
Geometric Topology
2009-03-16 v4
Abstract
Suppose M is a compact orientable irreducible 3-manifold with Heegaard splitting surfaces P and Q. Then either Q is isotopic to a possibly stabilized copy of P or the Hempel distance of the splitting P is no greater than twice the genus of Q. More generally, if P and Q are bicompressible but weakly incompressible connected closed separating surfaces in M then either a) P and Q can be well-separated or b) P and Q are isotopic or c) the Hempel distance of P is no greater than twice the genus of Q.
Cite
@article{arxiv.math/0501140,
title = {Alternate Heegaard genus bounds distance},
author = {Martin Scharlemann and Maggy Tomova},
journal= {arXiv preprint arXiv:math/0501140},
year = {2009}
}
Comments
This is the version published by Geometry & Topology on 4 May 2006 (V4: typesetting correction)