Saddle Tangencies and the Distance of Heegaard Splittings
نویسنده
چکیده
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 P ∩ Q = ∅ after an isotopy or the Hempel distance d(P ) ≤ 2genus(Q). This theorem can be naturally extended to bicompressible but weakly incompressible surfaces.
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