Heegaard genera of high distance are additive under annulus sum

Fengling Li; Guoqiu Yang; Fengchun Lei

doi:10.1016/j.topol.2010.02.009

Heegaard genera of high distance are additive under annulus sum

Fengling Li
, Guoqiu Yang
, Fengchun Lei^*

^*Corresponding author for this work

School of Sciences

Harbin Institute of Technology
Dalian University of Technology

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

7 Scopus citations

Abstract

Let M_i be a compact orientable 3-manifold, and A_i a non-separating incompressible annulus on ∂ M_i, i = 1, 2. Let h : A₁ → A₂ be a homeomorphism, and M = M₁ ∪_h M₂ the annulus sum of M₁ and M₂ along A₁ and A₂. In the present paper, we show that if M_i has a Heegaard splitting V_i ∪_Si W_i with distance d (S_i) ≥ 2 g (M_i) + 3 for i = 1, 2, then g (M) = g (M₁) + g (M₂). Moreover, if g (F_i) ≥ 2, i = 1, 2, then the minimal Heegaard splitting of M is unique.

Original language	English
Pages (from-to)	1188-1194
Number of pages	7
Journal	Topology and its Applications
Volume	157
Issue number	7
DOIs	https://doi.org/10.1016/j.topol.2010.02.009
State	Published - 1 May 2010

Keywords

Annulus sum
Distance
Heegaard genus

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title = "Heegaard genera of high distance are additive under annulus sum",

abstract = "Let Mi be a compact orientable 3-manifold, and Ai a non-separating incompressible annulus on ∂ Mi, i = 1, 2. Let h : A1 → A2 be a homeomorphism, and M = M1 ∪h M2 the annulus sum of M1 and M2 along A1 and A2. In the present paper, we show that if Mi has a Heegaard splitting Vi ∪Si Wi with distance d (Si) ≥ 2 g (Mi) + 3 for i = 1, 2, then g (M) = g (M1) + g (M2). Moreover, if g (Fi) ≥ 2, i = 1, 2, then the minimal Heegaard splitting of M is unique.",

keywords = "Annulus sum, Distance, Heegaard genus",

author = "Fengling Li and Guoqiu Yang and Fengchun Lei",

year = "2010",

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doi = "10.1016/j.topol.2010.02.009",

language = "英语",

volume = "157",

pages = "1188--1194",

journal = "Topology and its Applications",

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TY - JOUR

T1 - Heegaard genera of high distance are additive under annulus sum

AU - Li, Fengling

AU - Yang, Guoqiu

AU - Lei, Fengchun

PY - 2010/5/1

Y1 - 2010/5/1

N2 - Let Mi be a compact orientable 3-manifold, and Ai a non-separating incompressible annulus on ∂ Mi, i = 1, 2. Let h : A1 → A2 be a homeomorphism, and M = M1 ∪h M2 the annulus sum of M1 and M2 along A1 and A2. In the present paper, we show that if Mi has a Heegaard splitting Vi ∪Si Wi with distance d (Si) ≥ 2 g (Mi) + 3 for i = 1, 2, then g (M) = g (M1) + g (M2). Moreover, if g (Fi) ≥ 2, i = 1, 2, then the minimal Heegaard splitting of M is unique.

AB - Let Mi be a compact orientable 3-manifold, and Ai a non-separating incompressible annulus on ∂ Mi, i = 1, 2. Let h : A1 → A2 be a homeomorphism, and M = M1 ∪h M2 the annulus sum of M1 and M2 along A1 and A2. In the present paper, we show that if Mi has a Heegaard splitting Vi ∪Si Wi with distance d (Si) ≥ 2 g (Mi) + 3 for i = 1, 2, then g (M) = g (M1) + g (M2). Moreover, if g (Fi) ≥ 2, i = 1, 2, then the minimal Heegaard splitting of M is unique.

KW - Annulus sum

KW - Distance

KW - Heegaard genus

UR - https://www.scopus.com/pages/publications/77949492679

U2 - 10.1016/j.topol.2010.02.009

DO - 10.1016/j.topol.2010.02.009

M3 - 文章

AN - SCOPUS:77949492679

SN - 0166-8641

VL - 157

SP - 1188

EP - 1194

JO - Topology and its Applications

JF - Topology and its Applications

IS - 7

ER -

Heegaard genera of high distance are additive under annulus sum

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