The amalgamation of high distance Heegaard splittings is always efficient

Tsuyoshi Kobayashi; Ruifeng Qiu

doi:10.1007/s00208-008-0214-7

The amalgamation of high distance Heegaard splittings is always efficient

Tsuyoshi Kobayashi
, Ruifeng Qiu^*

^*此作品的通讯作者

Nara Women's University
Dalian University of Technology

科研成果: 期刊稿件 › 文章 › 同行评审

41 引用（Scopus）

摘要

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 ∪_si W_i be a Heegaard splitting for i = 1, 2. We denote by d(S _i ) the distance of V_i ∪_si 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_i ∪_si W_i and V₂ ∪_s2 W₂.

源语言	英语
页（从-至）	707-715
页数	9
期刊	Mathematische Annalen
卷	341
期	3
DOI	https://doi.org/10.1007/s00208-008-0214-7
出版状态	已出版 - 7月 2008
已对外发布	是

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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 Mi = Vi ∪si Wi be a Heegaard splitting for i = 1, 2. We denote by d(S i ) the distance of Vi ∪si Wi. 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 Vi ∪si Wi and V2 ∪s2 W2.",

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N2 - 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 Mi = Vi ∪si Wi be a Heegaard splitting for i = 1, 2. We denote by d(S i ) the distance of Vi ∪si Wi. 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 Vi ∪si Wi and V2 ∪s2 W2.

AB - 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 Mi = Vi ∪si Wi be a Heegaard splitting for i = 1, 2. We denote by d(S i ) the distance of Vi ∪si Wi. 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 Vi ∪si Wi and V2 ∪s2 W2.

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SN - 0025-5831

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SP - 707

EP - 715

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 3

ER -

The amalgamation of high distance Heegaard splittings is always efficient

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