Abstract
Let and be orientable irreducible –manifolds with connected boundary and suppose . Let be a closed –manifold obtained by gluing to along the boundary. We show that if the gluing homeomorphism is sufficiently complicated, then is not homeomorphic to and all small-genus Heegaard splittings of are standard in a certain sense. In particular, , where denotes the Heegaard genus of . This theorem is also true for certain manifolds with multiple boundary components.
Citation
Tao Li. "Heegaard surfaces and the distance of amalgamation." Geom. Topol. 14 (4) 1871 - 1919, 2010. https://doi.org/10.2140/gt.2010.14.1871
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