On the Heegaard splittings of amalgamated 3-manifolds

Details On the Heegaard splittings of amalgamated 3-manifolds On the Heegaard splittings of amalgamated 3-manifolds

2007-01-14

arxiv.org/abs/math/0701395v2

Geom. Topol. Monogr. 12 (2007) 157-190

Mathematics

Geometric Topology

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

Scientific paper

10.2140/gtm.2007.12.157

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.

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