Geometry & Topology

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

Tao Li

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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
Received: 15 June 2010
Revised: 16 May 2011
Accepted: 8 May 2011
First available in Project Euclid: 20 December 2017

Permanent link to this document
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

Subjects
Primary: 57N10: Topology of general 3-manifolds [See also 57Mxx]
Secondary: 57M50: Geometric structures on low-dimensional manifolds 57M5057M25

Keywords
Heegaard splitting algorithm Heegaard genus branched surface

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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