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

^*此作品的通讯作者

数学科学学院

Dalian University of Technology
Lanzhou University

科研成果: 期刊稿件 › 文章 › 同行评审

21 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	406-411
页数	6
期刊	Topology and its Applications
卷	160
期	2
DOI	https://doi.org/10.1016/j.topol.2012.11.020
出版状态	已出版 - 2013

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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",

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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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