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2007 Saddle tangencies and the distance of Heegaard splittings
Tao Li
Algebr. Geom. Topol. 7(2): 1119-1134 (2007). DOI: 10.2140/agt.2007.7.1119

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.

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Tao Li. "Saddle tangencies and the distance of Heegaard splittings." Algebr. Geom. Topol. 7 (2) 1119 - 1134, 2007. https://doi.org/10.2140/agt.2007.7.1119

Information

Received: 7 January 2007; Revised: 1 June 2007; Accepted: 25 July 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1134.57005
MathSciNet: MR2336252
Digital Object Identifier: 10.2140/agt.2007.7.1119

Subjects:
Primary: 57N10
Secondary: 57M50

Rights: Copyright © 2007 Mathematical Sciences Publishers

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Vol.7 • No. 2 • 2007
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