On the Heegaard splittings of amalgamated 3-manifolds

Tao Li

doi:10.2140/gtm.2007.12.157

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On the Heegaard splittings of amalgamated 3-manifolds

Tao Li

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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.

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Tao Li. 2009-03-31. On the Heegaard splittings of amalgamated 3-manifolds. https://doi.org/10.2140/gtm.2007.12.157

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