#### Volume 15, issue 2 (2011)

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

### Tao Li

Geometry & Topology 15 (2011) 1029–1106
##### 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
##### 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/