An algorithm to determine the Heegaard genus of a 3-manifold

Tao Li

Published 2010-02-09, updated 2010-06-15Version 2

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.