## Algebraic & Geometric Topology

### Saddle tangencies and the distance of Heegaard splittings

Tao Li

#### 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.

#### Article information

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

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

https://projecteuclid.org/euclid.agt/1513796717

Digital Object Identifier
doi:10.2140/agt.2007.7.1119

Mathematical Reviews number (MathSciNet)
MR2336252

Zentralblatt MATH identifier
1134.57005

#### Citation

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. https://projecteuclid.org/euclid.agt/1513796717

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