Unstabilized self-amalgamation of a Heegaard splitting

Yanqing Zou; Kun Du; Qilong Guo; Ruifeng Qiu

doi:10.1016/j.topol.2012.11.020

Unstabilized self-amalgamation of a Heegaard splitting

Yanqing Zou^*
, Kun Du
, Qilong Guo
, Ruifeng Qiu

^*Corresponding author for this work

School of Mathematical Sciences

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

21 Scopus citations

Abstract

Let M be a compact orientable 3-manifold, M=V∪_SW be a Heegaard splitting of M, and F₁, F₂ be two homeomorphic components of ∂M lying in the minus boundary of W. Let M^* be the manifold obtained from M by gluing F₁ and F₂ together. Then M^* has a natural Heegaard splitting called the self-amalgamation of V∪_SW. In this paper, we prove that the self-amalgamation of a distance at least 3 Heegaard splitting is unstabilized. There are some examples to show that the lower bound 3 is the best.

Original language	English
Pages (from-to)	406-411
Number of pages	6
Journal	Topology and its Applications
Volume	160
Issue number	2
DOIs	https://doi.org/10.1016/j.topol.2012.11.020
State	Published - 2013

Keywords

Distance
Heegaard splitting
Stabilization

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10.1016/j.topol.2012.11.020

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title = "Unstabilized self-amalgamation of a Heegaard splitting",

abstract = "Let M be a compact orientable 3-manifold, M=V∪SW be a Heegaard splitting of M, and F1, F2 be two homeomorphic components of ∂M lying in the minus boundary of W. Let M* be the manifold obtained from M by gluing F1 and F2 together. Then M* has a natural Heegaard splitting called the self-amalgamation of V∪SW. In this paper, we prove that the self-amalgamation of a distance at least 3 Heegaard splitting is unstabilized. There are some examples to show that the lower bound 3 is the best.",

keywords = "Distance, Heegaard splitting, Stabilization",

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

year = "2013",

doi = "10.1016/j.topol.2012.11.020",

language = "英语",

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T1 - Unstabilized self-amalgamation of a Heegaard splitting

AU - Zou, Yanqing

AU - Du, Kun

AU - Guo, Qilong

AU - Qiu, Ruifeng

PY - 2013

Y1 - 2013

N2 - Let M be a compact orientable 3-manifold, M=V∪SW be a Heegaard splitting of M, and F1, F2 be two homeomorphic components of ∂M lying in the minus boundary of W. Let M* be the manifold obtained from M by gluing F1 and F2 together. Then M* has a natural Heegaard splitting called the self-amalgamation of V∪SW. In this paper, we prove that the self-amalgamation of a distance at least 3 Heegaard splitting is unstabilized. There are some examples to show that the lower bound 3 is the best.

AB - Let M be a compact orientable 3-manifold, M=V∪SW be a Heegaard splitting of M, and F1, F2 be two homeomorphic components of ∂M lying in the minus boundary of W. Let M* be the manifold obtained from M by gluing F1 and F2 together. Then M* has a natural Heegaard splitting called the self-amalgamation of V∪SW. In this paper, we prove that the self-amalgamation of a distance at least 3 Heegaard splitting is unstabilized. There are some examples to show that the lower bound 3 is the best.

KW - Distance

KW - Heegaard splitting

KW - Stabilization

UR - https://www.scopus.com/pages/publications/84871408065

U2 - 10.1016/j.topol.2012.11.020

DO - 10.1016/j.topol.2012.11.020

M3 - 文章

AN - SCOPUS:84871408065

SN - 0166-8641

VL - 160

SP - 406

EP - 411

JO - Topology and its Applications

JF - Topology and its Applications

IS - 2

ER -

Unstabilized self-amalgamation of a Heegaard splitting

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Keywords

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