The Heegaard genera of surface sums

Ruifeng Qiu; Shicheng Wang; Mingxing Zhang

doi:10.1016/j.topol.2010.02.015

The Heegaard genera of surface sums

Ruifeng Qiu^*
, Shicheng Wang
, Mingxing Zhang

^*Corresponding author for this work

School of Mathematical Sciences

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

7 Scopus citations

Abstract

Let M be a compact orientable 3-manifold, and let F be a separating (resp. non-separating) incompressible surface in M which cuts M into two 3-manifolds M₁ and M₂ (resp. a manifold M₁). Then M is called the surface sum (resp. self surface sum) of M₁ and M₂ (resp. M₁) along F, denoted by M=M₁∪_FM₂ (resp. M=M₁∪_F). In this paper, we will study how g(M) is related to χ(F), g(M₁) and g(M₂) when both M₁ and M₂ have high distance Heegaard splittings.

Original language	English
Pages (from-to)	1593-1601
Number of pages	9
Journal	Topology and its Applications
Volume	157
Issue number	9
DOIs	https://doi.org/10.1016/j.topol.2010.02.015
State	Published - Jun 2010

Keywords

(Self) surface sum
Heegaard distance and genus
Weakly incompressible surfaces

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10.1016/j.topol.2010.02.015

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title = "The Heegaard genera of surface sums",

abstract = "Let M be a compact orientable 3-manifold, and let F be a separating (resp. non-separating) incompressible surface in M which cuts M into two 3-manifolds M1 and M2 (resp. a manifold M1). Then M is called the surface sum (resp. self surface sum) of M1 and M2 (resp. M1) along F, denoted by M=M1∪FM2 (resp. M=M1∪F). In this paper, we will study how g(M) is related to χ(F), g(M1) and g(M2) when both M1 and M2 have high distance Heegaard splittings.",

keywords = "(Self) surface sum, Heegaard distance and genus, Weakly incompressible surfaces",

author = "Ruifeng Qiu and Shicheng Wang and Mingxing Zhang",

year = "2010",

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T1 - The Heegaard genera of surface sums

AU - Qiu, Ruifeng

AU - Wang, Shicheng

AU - Zhang, Mingxing

PY - 2010/6

Y1 - 2010/6

N2 - Let M be a compact orientable 3-manifold, and let F be a separating (resp. non-separating) incompressible surface in M which cuts M into two 3-manifolds M1 and M2 (resp. a manifold M1). Then M is called the surface sum (resp. self surface sum) of M1 and M2 (resp. M1) along F, denoted by M=M1∪FM2 (resp. M=M1∪F). In this paper, we will study how g(M) is related to χ(F), g(M1) and g(M2) when both M1 and M2 have high distance Heegaard splittings.

AB - Let M be a compact orientable 3-manifold, and let F be a separating (resp. non-separating) incompressible surface in M which cuts M into two 3-manifolds M1 and M2 (resp. a manifold M1). Then M is called the surface sum (resp. self surface sum) of M1 and M2 (resp. M1) along F, denoted by M=M1∪FM2 (resp. M=M1∪F). In this paper, we will study how g(M) is related to χ(F), g(M1) and g(M2) when both M1 and M2 have high distance Heegaard splittings.

KW - (Self) surface sum

KW - Heegaard distance and genus

KW - Weakly incompressible surfaces

UR - https://www.scopus.com/pages/publications/77952888541

U2 - 10.1016/j.topol.2010.02.015

DO - 10.1016/j.topol.2010.02.015

M3 - 文章

AN - SCOPUS:77952888541

SN - 0166-8641

VL - 157

SP - 1593

EP - 1601

JO - Topology and its Applications

JF - Topology and its Applications

IS - 9

ER -

The Heegaard genera of surface sums

Abstract

Keywords

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