A sufficient condition for the genus of an amalgamated 3-manifold not to go down

Feng Ling Li; Guo Qiu Yang; Feng Chun Lei

doi:10.1007/s11425-010-3130-8

A sufficient condition for the genus of an amalgamated 3-manifold not to go down

Feng Ling Li
, Guo Qiu Yang
, Feng Chun Lei

School of Sciences

Harbin Institute of Technology
Dalian University of Technology

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

3 Scopus citations

Abstract

Let M_i be a connected, compact, orientable 3-manifold, F_i a boundary component of M_i with g(F_i) ≥ 2, i = 1, 2, and F₁ ≊ F₂. Let φ: F₁ → F₂ be a homeomorphism, and M = M₁ ∪_φM₂, F = F₂ = φ(F₁). Then it is known that g(M) ≤ g(M₁)+g(M₂)-g(F). In the present paper, we give a sufficient condition for the genus of an amalgamated 3-manifold not to go down as follows: Suppose that there is no essential surface with boundary (Q_i, ∂Q_i) in (M_i, F_i) satisfying χ(Q_i) > 3 - 2g(M_i), i = 1, 2. Then g(M) = g(M₁) + g(M₂) - g(F).

Original language	English
Pages (from-to)	1697-1702
Number of pages	6
Journal	Science China Mathematics
Volume	53
Issue number	7
DOIs	https://doi.org/10.1007/s11425-010-3130-8
State	Published - 2010

Keywords

Amalgamation
Essential surface
Heegaard genus

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10.1007/s11425-010-3130-8

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title = "A sufficient condition for the genus of an amalgamated 3-manifold not to go down",

abstract = "Let Mi be a connected, compact, orientable 3-manifold, Fi a boundary component of Mi with g(Fi) ≥ 2, i = 1, 2, and F1 ≊ F2. Let φ: F1 → F2 be a homeomorphism, and M = M1 ∪φM2, F = F2 = φ(F1). Then it is known that g(M) ≤ g(M1)+g(M2)-g(F). In the present paper, we give a sufficient condition for the genus of an amalgamated 3-manifold not to go down as follows: Suppose that there is no essential surface with boundary (Qi, ∂Qi) in (Mi, Fi) satisfying χ(Qi) > 3 - 2g(Mi), i = 1, 2. Then g(M) = g(M1) + g(M2) - g(F).",

keywords = "Amalgamation, Essential surface, Heegaard genus",

author = "Li, \{Feng Ling\} and Yang, \{Guo Qiu\} and Lei, \{Feng Chun\}",

year = "2010",

doi = "10.1007/s11425-010-3130-8",

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pages = "1697--1702",

journal = "Science China Mathematics",

issn = "1674-7283",

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}

TY - JOUR

T1 - A sufficient condition for the genus of an amalgamated 3-manifold not to go down

AU - Li, Feng Ling

AU - Yang, Guo Qiu

AU - Lei, Feng Chun

PY - 2010

Y1 - 2010

N2 - Let Mi be a connected, compact, orientable 3-manifold, Fi a boundary component of Mi with g(Fi) ≥ 2, i = 1, 2, and F1 ≊ F2. Let φ: F1 → F2 be a homeomorphism, and M = M1 ∪φM2, F = F2 = φ(F1). Then it is known that g(M) ≤ g(M1)+g(M2)-g(F). In the present paper, we give a sufficient condition for the genus of an amalgamated 3-manifold not to go down as follows: Suppose that there is no essential surface with boundary (Qi, ∂Qi) in (Mi, Fi) satisfying χ(Qi) > 3 - 2g(Mi), i = 1, 2. Then g(M) = g(M1) + g(M2) - g(F).

AB - Let Mi be a connected, compact, orientable 3-manifold, Fi a boundary component of Mi with g(Fi) ≥ 2, i = 1, 2, and F1 ≊ F2. Let φ: F1 → F2 be a homeomorphism, and M = M1 ∪φM2, F = F2 = φ(F1). Then it is known that g(M) ≤ g(M1)+g(M2)-g(F). In the present paper, we give a sufficient condition for the genus of an amalgamated 3-manifold not to go down as follows: Suppose that there is no essential surface with boundary (Qi, ∂Qi) in (Mi, Fi) satisfying χ(Qi) > 3 - 2g(Mi), i = 1, 2. Then g(M) = g(M1) + g(M2) - g(F).

KW - Amalgamation

KW - Essential surface

KW - Heegaard genus

UR - https://www.scopus.com/pages/publications/77954460074

U2 - 10.1007/s11425-010-3130-8

DO - 10.1007/s11425-010-3130-8

M3 - 文章

AN - SCOPUS:77954460074

SN - 1674-7283

VL - 53

SP - 1697

EP - 1702

JO - Science China Mathematics

JF - Science China Mathematics

IS - 7

ER -

A sufficient condition for the genus of an amalgamated 3-manifold not to go down

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Keywords

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