Algebraic & Geometric Topology 7 (2007) 1119–1134

DOI: 10.2140/agt.2007.7.1119

arXiv: math.GT/0701396

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)≤ 2genus(Q) or P is isotopic to Q. This theorem can be naturally extended to bicompressible but weakly incompressible surfaces.

Keywords

Heegaard splitting, incompressible surface, curve complex, sample layout

Mathematical Subject Classification

Primary: 57N10

Secondary: 57M50

References

Publication

Received: 7 January 2007
Revised: 1 June 2007
Accepted: 25 July 2007
Published: 2 August 2007

Authors