Heegaard genera of annular 3-manifolds

Kun Du; Jiming Ma; Ruifeng Qiu; Mingxing Zhang

doi:10.1142/S0218216511009418

Heegaard genera of annular 3-manifolds

Kun Du^*
, Jiming Ma
, Ruifeng Qiu
, Mingxing Zhang

^*Corresponding author for this work

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

9 Scopus citations

Abstract

Let M be a compact orientable 3-manifold, and A an essential annulus which cuts M into two 3-manifolds M₁ and M₂. We denote by g(M) the Heegaard genus of M. In this paper, we will give a lower bound to g(M) when M_i contains no bounded essential surfaces with large Euler's characteristic, where all boundary components of the essential surfaces lie in A.

Original language	English
Pages (from-to)	547-566
Number of pages	20
Journal	Journal of Knot Theory and its Ramifications
Volume	20
Issue number	4
DOIs	https://doi.org/10.1142/S0218216511009418
State	Published - Apr 2011
Externally published	Yes

Keywords

Heegaard genera
primitive
strongly irreducible

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10.1142/S0218216511009418

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title = "Heegaard genera of annular 3-manifolds",

abstract = "Let M be a compact orientable 3-manifold, and A an essential annulus which cuts M into two 3-manifolds M1 and M2. We denote by g(M) the Heegaard genus of M. In this paper, we will give a lower bound to g(M) when Mi contains no bounded essential surfaces with large Euler's characteristic, where all boundary components of the essential surfaces lie in A.",

keywords = "Heegaard genera, primitive, strongly irreducible",

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T1 - Heegaard genera of annular 3-manifolds

AU - Du, Kun

AU - Ma, Jiming

AU - Qiu, Ruifeng

AU - Zhang, Mingxing

PY - 2011/4

Y1 - 2011/4

N2 - Let M be a compact orientable 3-manifold, and A an essential annulus which cuts M into two 3-manifolds M1 and M2. We denote by g(M) the Heegaard genus of M. In this paper, we will give a lower bound to g(M) when Mi contains no bounded essential surfaces with large Euler's characteristic, where all boundary components of the essential surfaces lie in A.

AB - Let M be a compact orientable 3-manifold, and A an essential annulus which cuts M into two 3-manifolds M1 and M2. We denote by g(M) the Heegaard genus of M. In this paper, we will give a lower bound to g(M) when Mi contains no bounded essential surfaces with large Euler's characteristic, where all boundary components of the essential surfaces lie in A.

KW - Heegaard genera

KW - primitive

KW - strongly irreducible

UR - https://www.scopus.com/pages/publications/79957503741

U2 - 10.1142/S0218216511009418

DO - 10.1142/S0218216511009418

M3 - 文章

AN - SCOPUS:79957503741

SN - 0218-2165

VL - 20

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EP - 566

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

IS - 4

ER -

Heegaard genera of annular 3-manifolds

Abstract

Keywords

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