(untitled) (Communications in Mathematical Research, 2021)
Let M_i be a compact orientable 3-manifold, and A_i a non-separating incompressible annulus on a component of ∂M_i, say F_i , i = 1, 2. Let h : A_1 → A_2 be a homeomorphism, and M = M_1 ∪_h M_2, the annulus sum of M_1 and M_2 along A_1 and A_2. Suppose that M_i has a Heegaard splitting V_i ∪_S_i W_i with distance d(S_i) ≥ 2g(M_i) + 2g(F_3−i) + 1, i = 1, 2. Then g(M) = g(M_1) + g(M_2), and the minimal Heegaard splitting of M is unique, which is the natural Heegaard splitting of M induced from V_1 ∪_S_1 W_1 and V_2 ∪_S_2 W_2.