A note on Heegaard splittings of amalgamated 3-manifolds

Abstract

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 M ₁ and M ₂. If M _i has a minimal Heegaard splitting M_i = $V_i \cup _{H_i }$W_i with d(H ₁) + d(H ₂) ≥ 2(g(M ₁) + g(M ₂) − g(F)) + 1, then g(M) = g(M 1) + g(M 2) − g(F).

Keywords

Distance / Stabilization / Strongly irreducible

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