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 M1 and M2 be simple 3-manifolds with connected boundary of genus g>0. If M1 and M2 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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