摘要
Let M be a compact orientable irreducible 3-manifold, and F be an essential connected closed surface in M which cuts M into two manifolds M1 and M2. If Mi has a minimal Heegaard splitting Mi = Vi∪Hi Wi with d（H1） ＋ d（H2） ≥ 2（g（M0 ＋ g（M2） - g（F）） ＋ 1, then g（M） = g（M1） ＋ g（M2） - g（F）.
基金
Project supported by the National Natural Science Foundation of China(No.10625102)
