A formula on Heegaard genus of self-amalgamated 3-manifolds

Qilong Guo; Yanqing Zou

doi:10.1016/j.topol.2011.12.007

A formula on Heegaard genus of self-amalgamated 3-manifolds

Qilong Guo, Yanqing Zou

Dalian University of Technology

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

1 Scopus citations

Abstract

Let M be an orientable compact irreducible and ∂-irreducible 3-manifold, and suppose ∂M consists of two boundary components F ₁ and F ₂ with g(F ₁)=g(F ₂)>1. Let M _f be the closed orientable 3-manifold obtained by identifying F ₁ and F ₂ via a homeomorphism f:F ₁→F ₂. With the assumption that M is small or g(M, F ₁)=g(M)+g(F ₁), we show that if f is sufficiently complicated, then g(M _f)=g(M, ∂M)+1.

Original language	English
Pages (from-to)	1300-1303
Number of pages	4
Journal	Topology and its Applications
Volume	159
Issue number	5
DOIs	https://doi.org/10.1016/j.topol.2011.12.007
State	Published - 15 Mar 2012
Externally published	Yes

Keywords

Heegaard splitting
Self-amalgamated
Sufficiently complicated

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abstract = "Let M be an orientable compact irreducible and ∂-irreducible 3-manifold, and suppose ∂M consists of two boundary components F 1 and F 2 with g(F 1)=g(F 2)>1. Let M f be the closed orientable 3-manifold obtained by identifying F 1 and F 2 via a homeomorphism f:F 1→F 2. With the assumption that M is small or g(M, F 1)=g(M)+g(F 1), we show that if f is sufficiently complicated, then g(M f)=g(M, ∂M)+1.",

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T1 - A formula on Heegaard genus of self-amalgamated 3-manifolds

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AU - Zou, Yanqing

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N2 - Let M be an orientable compact irreducible and ∂-irreducible 3-manifold, and suppose ∂M consists of two boundary components F 1 and F 2 with g(F 1)=g(F 2)>1. Let M f be the closed orientable 3-manifold obtained by identifying F 1 and F 2 via a homeomorphism f:F 1→F 2. With the assumption that M is small or g(M, F 1)=g(M)+g(F 1), we show that if f is sufficiently complicated, then g(M f)=g(M, ∂M)+1.

AB - Let M be an orientable compact irreducible and ∂-irreducible 3-manifold, and suppose ∂M consists of two boundary components F 1 and F 2 with g(F 1)=g(F 2)>1. Let M f be the closed orientable 3-manifold obtained by identifying F 1 and F 2 via a homeomorphism f:F 1→F 2. With the assumption that M is small or g(M, F 1)=g(M)+g(F 1), we show that if f is sufficiently complicated, then g(M f)=g(M, ∂M)+1.

KW - Heegaard splitting

KW - Self-amalgamated

KW - Sufficiently complicated

UR - https://www.scopus.com/pages/publications/84856349410

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DO - 10.1016/j.topol.2011.12.007

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SN - 0166-8641

VL - 159

SP - 1300

EP - 1303

JO - Topology and its Applications

JF - Topology and its Applications

IS - 5

ER -

A formula on Heegaard genus of self-amalgamated 3-manifolds

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Keywords

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