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The amalgamation of high distance Heegaard splittings is always efficient

Authors:	Tsuyoshi Kobayashi Ruifeng Qiu

Institution:	(1) Graduate School of Humanities and Sciences, Nara Women’s University, Nara, Japan;(2) Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning, China

Abstract:	Let M be a compact orientable manifold, and F be an essential closed surface which cuts M into two 3-manifolds M ₁ and M ₂. Let ${M_{i}=V_{i}\cup_{S_{i}} W_{i}}$ be a Heegaard splitting for i = 1, 2. We denote by d(S _i) the distance of ${V_{i}\cup_{S_{i}} W_{i}}$ . If d(S ₁), d(S ₂) ≥ 2(g(M ₁) + g(M ₂) − g(F)), then M has a unique minimal Heegaard splitting up to isotopy, i.e. the amalgamation of ${V_{1}\cup_{S_{1}} W_{1}}$ and ${V_{2}\cup_{S_{2}} W_{2}}$ . Ruifeng Qiu is supported by NSFC(10625102).

Keywords:	57M25
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