## Geometry & Topology

### An algorithm to determine the Heegaard genus of a $3$–manifold

Tao Li

#### Abstract

We give an algorithmic proof of the theorem that a closed orientable irreducible and atoroidal $3$–manifold has only finitely many Heegaard splittings in each genus, up to isotopy. The proof gives an algorithm to determine the Heegaard genus of an atoroidal $3$–manifold.

#### Article information

Source
Geom. Topol., Volume 15, Number 2 (2011), 1029-1106.

Dates
Revised: 16 May 2011
Accepted: 8 May 2011
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732311

Digital Object Identifier
doi:10.2140/gt.2011.15.1029

Mathematical Reviews number (MathSciNet)
MR2821570

Zentralblatt MATH identifier
1221.57034

#### Citation

Li, Tao. An algorithm to determine the Heegaard genus of a $3$–manifold. Geom. Topol. 15 (2011), no. 2, 1029--1106. doi:10.2140/gt.2011.15.1029. https://projecteuclid.org/euclid.gt/1513732311

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