Heegaard Surfaces and the Distance of Amalgamation
نویسنده
چکیده
Let M1 and M2 be orientable irreducible 3–manifolds with connected boundary and suppose ∂M1 = ∂M2. Let M be a closed 3–manifold obtained by gluing M1 to M2 along the boundary. We show that if the gluing homeomorphism is sufficiently complicated, then M is not homeomorphic to S and all small-genus Heegaard splittings of M are standard in a certain sense. In particular, g(M) = g(M1) + g(M2) − g(∂Mi), where g(M) denotes the Heegaard genus of M . This theorem can also be extended to manifolds with multiple boundary components.
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