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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 $V_2 ∪_{S_2} W_2$.
}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19180.html} }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 $V_2 ∪_{S_2} W_2$.