科研之友
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摘要
Let M be a connected orientable compact irreducible 3-manifold. Suppose that partial derivative M consists of two homeomorphic surfaces F-1 and F-2, and both F-1 and F-2 are compressible in M. Suppose furthermore that g(M, F-1) = g(M) + g(F-1), where g(M, F-1) is the Heegaard genus of M relative to F-1. Let M-f be the closed orientable 3-manifold obtained by identifying F-1 and F-2 using a homeomorphism f : F1 -> F2. The authors show that if f is sufficiently complicated, then g(Mf) = g(M, partial derivative M) + 1.
