On L-space knots obtained from unknotting arcs in alternating diagrams

Andrew Donald; Duncan McCoy; Faramarz Vafaee

On L-space knots obtained from unknotting arcs in alternating diagrams

Andrew Donald, Duncan McCoy, Faramarz Vafaee

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

Let D be a diagram of an alternating knot with unknotting number one. The branched double cover of S3 branched over D is an L-space obtained by half integral surgery on a knot KD. We denote the set of all such knots KD by D. We characterize when KD 2 D is a torus knot, a satellite knot or a hyperbolic knot. In a different direction, we show that for a given n > 0, there are only finitely many L-space knots in D with genus less than n.

Original language	English
Pages (from-to)	518-540
Number of pages	23
Journal	New York Journal of Mathematics
Volume	25
Early online date	20 Jun 2019
Publication status	E-pub ahead of print - 20 Jun 2019

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The acceptance date for this record is provisional and based upon the month of publication for the article.

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title = "On L-space knots obtained from unknotting arcs in alternating diagrams",

abstract = "Let D be a diagram of an alternating knot with unknotting number one. The branched double cover of S3 branched over D is an L-space obtained by half integral surgery on a knot KD. We denote the set of all such knots KD by D. We characterize when KD 2 D is a torus knot, a satellite knot or a hyperbolic knot. In a different direction, we show that for a given n > 0, there are only finitely many L-space knots in D with genus less than n.",

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AU - McCoy, Duncan

AU - Vafaee, Faramarz

N1 - The acceptance date for this record is provisional and based upon the month of publication for the article.

PY - 2019/6/20

Y1 - 2019/6/20

N2 - Let D be a diagram of an alternating knot with unknotting number one. The branched double cover of S3 branched over D is an L-space obtained by half integral surgery on a knot KD. We denote the set of all such knots KD by D. We characterize when KD 2 D is a torus knot, a satellite knot or a hyperbolic knot. In a different direction, we show that for a given n > 0, there are only finitely many L-space knots in D with genus less than n.

AB - Let D be a diagram of an alternating knot with unknotting number one. The branched double cover of S3 branched over D is an L-space obtained by half integral surgery on a knot KD. We denote the set of all such knots KD by D. We characterize when KD 2 D is a torus knot, a satellite knot or a hyperbolic knot. In a different direction, we show that for a given n > 0, there are only finitely many L-space knots in D with genus less than n.

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M3 - Article (Academic Journal)

AN - SCOPUS:85073268861

VL - 25

SP - 518

EP - 540

JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

SN - 1076-9803

ER -

On L-space knots obtained from unknotting arcs in alternating diagrams

Abstract

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