中文摘要：

Let Mibe a compact orientable 3-manifold, and Fibe an incompressible surface on Mi, i = 1, 2. Let f : F1→ F2be a homeomorphism, and M = M1∪fM2. In this paper,under certain assumptions for the attaching surface Fi, we show that if both M1and M2have Heegaard splittings with distance at least 2(g(M1) + g(M2)) + 1, then g(M) = g(M1) + g(M2).

英文摘要：

Let Mi be a compact orientable 3-manifold, and Fi be an incompressible surface on δMi, i -= 1,2. Let f ： F1 →F2 be a homeomorphism, and M = M1 UI M2. In this paper, under certain assumptions for the attaching surface Fi, we show that if both M1 and M2 have Heegaavd splittings with distance at least 2（g（M1）＋ g（M2））＋ 1, then g（M） = g（M1）＋g（M2）.