Alternate Heegaard genus bounds distance
arXiv:math/0501140 · doi:10.2140/gt.2006.10.593
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.
This is the version published by Geometry & Topology on 4 May 2006 (V4: typesetting correction)
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