A note on Heegaard genus of self-amalgamated 3-manifold

Qilong Guo; Ruifeng Qiu; Yanqing Zou

doi:10.1007/s11401-014-0877-1

A note on Heegaard genus of self-amalgamated 3-manifold

Qilong Guo^*
, Ruifeng Qiu
, Yanqing Zou

^*Corresponding author for this work

School of Mathematical Sciences

Dalian University of Technology

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

Abstract

Let M be a connected orientable compact irreducible 3-manifold. Suppose that ∂M consists of two homeomorphic surfaces F₁ and F₂, and both F₁ and F₂ are compressible in M. Suppose furthermore that g(M,F₁) = g(M) + g(F₁), where g(M,F₁) is the Heegaard genus of M relative to F₁. Let M_f be the closed orientable 3-manifold obtained by identifying F₁ and F₂ using a homeomorphism f: F₁ → F₂. The authors show that if f is sufficiently complicated, then g(M_f) = g(M,∂M) + 1.

Original language	English
Pages (from-to)	51-56
Number of pages	6
Journal	Chinese Annals of Mathematics. Series B
Volume	36
Issue number	1
DOIs	https://doi.org/10.1007/s11401-014-0877-1
State	Published - Jan 2015

Keywords

Heegaard splitting
Self-amalgamated
Sufficiently complicated

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title = "A note on Heegaard genus of self-amalgamated 3-manifold",

abstract = "Let M be a connected orientable compact irreducible 3-manifold. Suppose that ∂M consists of two homeomorphic surfaces F1 and F2, and both F1 and F2 are compressible in M. Suppose furthermore that g(M,F1) = g(M) + g(F1), where g(M,F1) is the Heegaard genus of M relative to F1. Let Mf be the closed orientable 3-manifold obtained by identifying F1 and F2 using a homeomorphism f: F1 → F2. The authors show that if f is sufficiently complicated, then g(Mf) = g(M,∂M) + 1.",

keywords = "Heegaard splitting, Self-amalgamated, Sufficiently complicated",

author = "Qilong Guo and Ruifeng Qiu and Yanqing Zou",

note = "Publisher Copyright: {\textcopyright} 2015, Fudan University and Springer-Verlag Berlin Heidelberg.",

year = "2015",

month = jan,

doi = "10.1007/s11401-014-0877-1",

language = "英语",

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T1 - A note on Heegaard genus of self-amalgamated 3-manifold

AU - Guo, Qilong

AU - Qiu, Ruifeng

AU - Zou, Yanqing

PY - 2015/1

Y1 - 2015/1

N2 - Let M be a connected orientable compact irreducible 3-manifold. Suppose that ∂M consists of two homeomorphic surfaces F1 and F2, and both F1 and F2 are compressible in M. Suppose furthermore that g(M,F1) = g(M) + g(F1), where g(M,F1) is the Heegaard genus of M relative to F1. Let Mf be the closed orientable 3-manifold obtained by identifying F1 and F2 using a homeomorphism f: F1 → F2. The authors show that if f is sufficiently complicated, then g(Mf) = g(M,∂M) + 1.

AB - Let M be a connected orientable compact irreducible 3-manifold. Suppose that ∂M consists of two homeomorphic surfaces F1 and F2, and both F1 and F2 are compressible in M. Suppose furthermore that g(M,F1) = g(M) + g(F1), where g(M,F1) is the Heegaard genus of M relative to F1. Let Mf be the closed orientable 3-manifold obtained by identifying F1 and F2 using a homeomorphism f: F1 → F2. The authors show that if f is sufficiently complicated, then g(Mf) = g(M,∂M) + 1.

KW - Heegaard splitting

KW - Self-amalgamated

KW - Sufficiently complicated

UR - https://www.scopus.com/pages/publications/84916599719

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DO - 10.1007/s11401-014-0877-1

M3 - 文章

AN - SCOPUS:84916599719

SN - 0252-9599

VL - 36

SP - 51

EP - 56

JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

IS - 1

ER -

A note on Heegaard genus of self-amalgamated 3-manifold

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Keywords

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