The distance between two separating, reducing slopes is at most 4

Mingxing Zhang; Ruifeng Qiu; Yannan Li

doi:10.1007/s00209-007-0147-y

The distance between two separating, reducing slopes is at most 4

Mingxing Zhang^*
, Ruifeng Qiu
, Yannan Li

^*Corresponding author for this work

Dalian University of Technology

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

6 Scopus citations

Abstract

Let M be a simple 3-manifold such that one component of ∂M, say F, has genus at least two. For a slope α on F, we denote by M(α) the manifold obtained by attaching a 2-handle to M along a regular neighborhood of α on F. If M(α) is reducible, then α is called a reducing slope. In this paper, we shall prove that the distance between two separating, reducing slopes on F is at most 4.

Original language	English
Pages (from-to)	799-810
Number of pages	12
Journal	Mathematische Zeitschrift
Volume	257
Issue number	4
DOIs	https://doi.org/10.1007/s00209-007-0147-y
State	Published - Dec 2007
Externally published	Yes

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title = "The distance between two separating, reducing slopes is at most 4",

abstract = "Let M be a simple 3-manifold such that one component of ∂M, say F, has genus at least two. For a slope α on F, we denote by M(α) the manifold obtained by attaching a 2-handle to M along a regular neighborhood of α on F. If M(α) is reducible, then α is called a reducing slope. In this paper, we shall prove that the distance between two separating, reducing slopes on F is at most 4.",

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AU - Zhang, Mingxing

AU - Qiu, Ruifeng

AU - Li, Yannan

PY - 2007/12

Y1 - 2007/12

N2 - Let M be a simple 3-manifold such that one component of ∂M, say F, has genus at least two. For a slope α on F, we denote by M(α) the manifold obtained by attaching a 2-handle to M along a regular neighborhood of α on F. If M(α) is reducible, then α is called a reducing slope. In this paper, we shall prove that the distance between two separating, reducing slopes on F is at most 4.

AB - Let M be a simple 3-manifold such that one component of ∂M, say F, has genus at least two. For a slope α on F, we denote by M(α) the manifold obtained by attaching a 2-handle to M along a regular neighborhood of α on F. If M(α) is reducible, then α is called a reducing slope. In this paper, we shall prove that the distance between two separating, reducing slopes on F is at most 4.

UR - https://www.scopus.com/pages/publications/34748892385

U2 - 10.1007/s00209-007-0147-y

DO - 10.1007/s00209-007-0147-y

M3 - 文章

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SP - 799

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JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 4

ER -

The distance between two separating, reducing slopes is at most 4

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