A quadratic bound on the number of boundary slopes of essential surfaces with bounded genus

Tao Li; Ruifeng Qiu; Shicheng Wang

doi:10.1007/s10711-009-9443-5

A quadratic bound on the number of boundary slopes of essential surfaces with bounded genus

Tao Li^*
, Ruifeng Qiu
, Shicheng Wang

^*Corresponding author for this work

School of Mathematical Sciences

Boston College
Peking University

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

1 Scopus citations

Abstract

Let M be an orientable 3-manifold with ∂M a single torus. We show that the number of boundary slopes of immersed essential surfaces with genus at most g is bounded by a quadratic function of g. In the hyperbolic case, this was proved earlier by Hass et al.

Original language	English
Pages (from-to)	131-138
Number of pages	8
Journal	Geometriae Dedicata
Volume	147
Issue number	1
DOIs	https://doi.org/10.1007/s10711-009-9443-5
State	Published - 2010

Keywords

Boundary slope
Essential surface

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10.1007/s10711-009-9443-5

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title = "A quadratic bound on the number of boundary slopes of essential surfaces with bounded genus",

abstract = "Let M be an orientable 3-manifold with ∂M a single torus. We show that the number of boundary slopes of immersed essential surfaces with genus at most g is bounded by a quadratic function of g. In the hyperbolic case, this was proved earlier by Hass et al.",

keywords = "Boundary slope, Essential surface",

author = "Tao Li and Ruifeng Qiu and Shicheng Wang",

year = "2010",

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T1 - A quadratic bound on the number of boundary slopes of essential surfaces with bounded genus

AU - Li, Tao

AU - Qiu, Ruifeng

AU - Wang, Shicheng

PY - 2010

Y1 - 2010

N2 - Let M be an orientable 3-manifold with ∂M a single torus. We show that the number of boundary slopes of immersed essential surfaces with genus at most g is bounded by a quadratic function of g. In the hyperbolic case, this was proved earlier by Hass et al.

AB - Let M be an orientable 3-manifold with ∂M a single torus. We show that the number of boundary slopes of immersed essential surfaces with genus at most g is bounded by a quadratic function of g. In the hyperbolic case, this was proved earlier by Hass et al.

KW - Boundary slope

KW - Essential surface

UR - https://www.scopus.com/pages/publications/77954243501

U2 - 10.1007/s10711-009-9443-5

DO - 10.1007/s10711-009-9443-5

M3 - 文章

AN - SCOPUS:77954243501

SN - 0046-5755

VL - 147

SP - 131

EP - 138

JO - Geometriae Dedicata

JF - Geometriae Dedicata

IS - 1

ER -

A quadratic bound on the number of boundary slopes of essential surfaces with bounded genus

Abstract

Keywords

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