Algebraic & Geometric Topology

Saddle tangencies and the distance of Heegaard splittings

Tao Li

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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.

Article information

Algebr. Geom. Topol., Volume 7, Number 2 (2007), 1119-1134.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57N10: Topology of general 3-manifolds [See also 57Mxx]
Secondary: 57M50: Geometric structures on low-dimensional manifolds

Heegaard splitting incompressible surface curve complex sample layout


Li, Tao. Saddle tangencies and the distance of Heegaard splittings. Algebr. Geom. Topol. 7 (2007), no. 2, 1119--1134. doi:10.2140/agt.2007.7.1119.

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