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^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

41 Scopus citations

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 ∪_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.

Original language	English
Pages (from-to)	707-715
Number of pages	9
Journal	Mathematische Annalen
Volume	341
Issue number	3
DOIs	https://doi.org/10.1007/s00208-008-0214-7
State	Published - Jul 2008
Externally published	Yes

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title = "The amalgamation of high distance Heegaard splittings is always efficient",

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.",

author = "Tsuyoshi Kobayashi and Ruifeng Qiu",

year = "2008",

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doi = "10.1007/s00208-008-0214-7",

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T1 - The amalgamation of high distance Heegaard splittings is always efficient

AU - Kobayashi, Tsuyoshi

AU - Qiu, Ruifeng

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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.

UR - https://www.scopus.com/pages/publications/42749088776

U2 - 10.1007/s00208-008-0214-7

DO - 10.1007/s00208-008-0214-7

M3 - 文章

AN - SCOPUS:42749088776

SN - 0025-5831

VL - 341

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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