Concordance of certain 3-braids and Gauss diagrams

2016/04/14 by Michael Brandenbursky, Brandenbursky, Michael
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.1604.04273

8 pages, 4 figures

arxiv created 2016/04/14 · arxiv updated 2016/04/15

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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