On the Heegaard splittings of amalgamated 3–manifolds
On the Heegaard splittings of amalgamated 3–manifolds
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 …