On the Heegaard splittings of amalgamated 3-manifolds

Abstract

We give a combinatorial proof of a theorem first proved by Souto which says the following. Let M_1 and M_2 be simple 3-manifolds with connected boundary of genus g>0. If M_1 and M_2 are glued via a complicated map, then every minimal Heegaard splitting of the resulting closed 3-manifold is an amalgamation. This proof also provides an algorithm to find a bound on the complexity of the gluing map.

This is the version published by Geometry & Topology Monographs on 3 December 2007

Cited by in corpus (2)

• Heegaard splittings of 3--manifolds (Haifa 2005): Problems
• Additivity of Heegaard genera of bounded surface sums