Saddle tangencies and the distance of Heegaard splittings

Tao Li

doi:10.2140/agt.2007.7.1119

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Saddle tangencies and the distance of Heegaard splittings

Tao Li

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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) <= 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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Tao Li. 2007-06-03. Saddle tangencies and the distance of Heegaard splittings. https://doi.org/10.2140/agt.2007.7.1119

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