2005/01/31 by Martin Scharlemann, Maggy Tomova · 1 citation
Mathematics · #math.GT #msc:57M50 #msc:57N10
paper · pdf · doi:10.2140/gt.2006.10.593
published as Geom. Topol. 10 (2006) 593-617 · This is the version published by Geometry & Topology on 4 May 2006 (V4: typesetting correction)
arxiv created 2009/03/15 · arxiv updated 2009/12/01
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.