On amalgamations of Heegaard splittings with high distance

Guoqiu Yang; Fengchun Lei

doi:10.1090/S0002-9939-08-09642-1

On amalgamations of Heegaard splittings with high distance

Guoqiu Yang^*
, Fengchun Lei

^*Corresponding author for this work

School of Sciences

Dalian University of Technology

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

22 Scopus citations

Abstract

Let M be a compact, orientable 3-manifold and F an essential closed surface which cuts M into M₁ and M₂. Suppose that M_i has a Heegaard splitting V_i ∪_Si. W _i with distance D(S_i) ≥ 2g(M_i) + 1, i =1, 2. Then g(M) = g(M₁)+g(M₂) - g(F), and the amalgamation of V₁ ∪_Si W₁ and V₂ ∪_S2 W₂ is the unique minimal Heegaard splitting of M up to isotopy.

Original language	English
Pages (from-to)	723-731
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	137
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-08-09642-1
State	Published - Feb 2009

Keywords

Amalgamation
Distance of Heegaard splitting
Minimal Heegaard splitting

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10.1090/S0002-9939-08-09642-1

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title = "On amalgamations of Heegaard splittings with high distance",

abstract = "Let M be a compact, orientable 3-manifold and F an essential closed surface which cuts M into M1 and M2. Suppose that Mi has a Heegaard splitting Vi ∪Si. W i with distance D(Si) ≥ 2g(Mi) + 1, i =1, 2. Then g(M) = g(M1)+g(M2) - g(F), and the amalgamation of V1 ∪Si W1 and V2 ∪S2 W2 is the unique minimal Heegaard splitting of M up to isotopy.",

keywords = "Amalgamation, Distance of Heegaard splitting, Minimal Heegaard splitting",

author = "Guoqiu Yang and Fengchun Lei",

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AU - Lei, Fengchun

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N2 - Let M be a compact, orientable 3-manifold and F an essential closed surface which cuts M into M1 and M2. Suppose that Mi has a Heegaard splitting Vi ∪Si. W i with distance D(Si) ≥ 2g(Mi) + 1, i =1, 2. Then g(M) = g(M1)+g(M2) - g(F), and the amalgamation of V1 ∪Si W1 and V2 ∪S2 W2 is the unique minimal Heegaard splitting of M up to isotopy.

AB - Let M be a compact, orientable 3-manifold and F an essential closed surface which cuts M into M1 and M2. Suppose that Mi has a Heegaard splitting Vi ∪Si. W i with distance D(Si) ≥ 2g(Mi) + 1, i =1, 2. Then g(M) = g(M1)+g(M2) - g(F), and the amalgamation of V1 ∪Si W1 and V2 ∪S2 W2 is the unique minimal Heegaard splitting of M up to isotopy.

KW - Amalgamation

KW - Distance of Heegaard splitting

KW - Minimal Heegaard splitting

UR - https://www.scopus.com/pages/publications/72949083176

U2 - 10.1090/S0002-9939-08-09642-1

DO - 10.1090/S0002-9939-08-09642-1

M3 - 文章

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EP - 731

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 2

ER -

On amalgamations of Heegaard splittings with high distance

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Keywords

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