The Heegaard Genus of Amalgamated 3-manifolds
نویسنده
چکیده
When studying Haken 3-manifolds, one is led naturally to the following construction: the amalgamation of two 3-manifolds M and M ′ via a homeomorphism between their boundaries. In this paper, we study the behaviour of Heegaard genus under this operation. We show that, provided the gluing homeomorphism is ‘sufficiently complicated’ and M and M ′ satisfy some standard conditions, then the Heegaard genus of the amalgamated manifold is completely determined by the Heegaard genus of M and M ′ and the genus of their common boundary. Recall that a 3-manifold is simple if it is compact, orientable, irreducible, atoroidal, acylindrical and has incompressible boundary. We denote the Heegaard genus of a 3-manifold M by g(M).
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