On maximal collections of essential annulu in a handlebody II

Xunbo Yin; Jingyan Tang; Fengchun Lei

doi:10.1142/S0218216509006914

On maximal collections of essential annulu in a handlebody II

Xunbo Yin^*
, Jingyan Tang
, Fengchun Lei

^*Corresponding author for this work

School of Mathematics

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

2 Scopus citations

Abstract

It is known that a maximal collection of essential annuli in H₂ could contain exactly 1, or 2, or at most 3 annuli, and a maximal collection of essential annuli in H_n with n < 3 can contains at most 4n - 5 annuli, and the bound is best possible. In the present paper, we show that a maximal collection of essential annuli in H_n with n < 3 contains at least two annuli, and for each m, 2 ≤ m ≤ 4n - 5, there exists a maximal collection of essential annuli in H_n which contains exactly m annuli.

Original language	English
Pages (from-to)	199-208
Number of pages	10
Journal	Journal of Knot Theory and its Ramifications
Volume	18
Issue number	2
DOIs	https://doi.org/10.1142/S0218216509006914
State	Published - Feb 2009

Keywords

Annulus-busting curve
Essential annuli
Handlebody
Maximal collection

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title = "On maximal collections of essential annulu in a handlebody II",

abstract = "It is known that a maximal collection of essential annuli in H2 could contain exactly 1, or 2, or at most 3 annuli, and a maximal collection of essential annuli in Hn with n < 3 can contains at most 4n - 5 annuli, and the bound is best possible. In the present paper, we show that a maximal collection of essential annuli in Hn with n < 3 contains at least two annuli, and for each m, 2 ≤ m ≤ 4n - 5, there exists a maximal collection of essential annuli in Hn which contains exactly m annuli.",

keywords = "Annulus-busting curve, Essential annuli, Handlebody, Maximal collection",

author = "Xunbo Yin and Jingyan Tang and Fengchun Lei",

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AU - Yin, Xunbo

AU - Tang, Jingyan

AU - Lei, Fengchun

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N2 - It is known that a maximal collection of essential annuli in H2 could contain exactly 1, or 2, or at most 3 annuli, and a maximal collection of essential annuli in Hn with n < 3 can contains at most 4n - 5 annuli, and the bound is best possible. In the present paper, we show that a maximal collection of essential annuli in Hn with n < 3 contains at least two annuli, and for each m, 2 ≤ m ≤ 4n - 5, there exists a maximal collection of essential annuli in Hn which contains exactly m annuli.

AB - It is known that a maximal collection of essential annuli in H2 could contain exactly 1, or 2, or at most 3 annuli, and a maximal collection of essential annuli in Hn with n < 3 can contains at most 4n - 5 annuli, and the bound is best possible. In the present paper, we show that a maximal collection of essential annuli in Hn with n < 3 contains at least two annuli, and for each m, 2 ≤ m ≤ 4n - 5, there exists a maximal collection of essential annuli in Hn which contains exactly m annuli.

KW - Annulus-busting curve

KW - Essential annuli

KW - Handlebody

KW - Maximal collection

UR - https://www.scopus.com/pages/publications/65249175681

U2 - 10.1142/S0218216509006914

DO - 10.1142/S0218216509006914

M3 - 文章

AN - SCOPUS:65249175681

SN - 0218-2165

VL - 18

SP - 199

EP - 208

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

IS - 2

ER -

On maximal collections of essential annulu in a handlebody II

Abstract

Keywords

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