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

Tao Li
Geometry & Topology 15 (2011) 1029–1106
DOI: 10.2140/gt.2011.15.1029
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.

Keywords
Heegaard splitting, algorithm, Heegaard genus, branched surface
Mathematical Subject Classification 2000
Primary: 57N10
Secondary: 57M50, 57M5057M25
References
Publication
Received: 15 June 2010
Revised: 16 May 2011
Accepted: 8 May 2011
Published: 22 June 2011
Proposed: Cameron Gordon
Seconded: Benson Farb, Martin Bridson
Authors
Tao Li
Department of Mathematics
Boston College
Chestnut Hill MA 02467
USA
http://www2.bc.edu/~taoli/