The Pants Sum of High Distance Heegaard Splittings

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).