Concordance of certain 3-braids and Gauss diagrams

Michael Brandenbursky

doi:10.1016/j.topol.2016.10.006

Concordance of certain 3-braids and Gauss diagrams

Michael Brandenbursky

Department of Mathematics

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

Abstract

Let β:=σ₁σ₂⁻¹ be a braid in B₃, where B₃ is the braid group on 3 strings and σ₁, σ₂ are the standard Artin generators. We use Gauss diagram formulas to show that for each natural number n not divisible by 3 the knot which is represented by the closure of the braid βⁿ is algebraically slice if and only if n is odd. As a consequence, we deduce some properties of Lucas numbers.

Original language	English
Pages (from-to)	180-185
Number of pages	6
Journal	Topology and its Applications
Volume	214
DOIs	https://doi.org/10.1016/j.topol.2016.10.006
State	Published - 1 Dec 2016

Keywords

Braids
Concordance
Gauss diagrams
Knots

ASJC Scopus subject areas

Geometry and Topology

Access to Document

10.1016/j.topol.2016.10.006

Cite this

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abstract = "Let β:=σ1σ2−1 be a braid in B3, where B3 is the braid group on 3 strings and σ1, σ2 are the standard Artin generators. We use Gauss diagram formulas to show that for each natural number n not divisible by 3 the knot which is represented by the closure of the braid βn is algebraically slice if and only if n is odd. As a consequence, we deduce some properties of Lucas numbers.",

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AB - Let β:=σ1σ2−1 be a braid in B3, where B3 is the braid group on 3 strings and σ1, σ2 are the standard Artin generators. We use Gauss diagram formulas to show that for each natural number n not divisible by 3 the knot which is represented by the closure of the braid βn is algebraically slice if and only if n is odd. As a consequence, we deduce some properties of Lucas numbers.

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KW - Gauss diagrams

KW - Knots

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ER -

Concordance of certain 3-braids and Gauss diagrams

Abstract

Keywords

ASJC Scopus subject areas

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