Saddle tangencies and the distance of Heegaard splittings

Details Saddle tangencies and the distance of Heegaard splittings Saddle tangencies and the distance of Heegaard splittings

2007-01-14

arxiv.org/abs/math/0701396v2

Mathematics

Geometric Topology

Scientific paper

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.

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