Concordance of certain 3-braids and Gauss diagrams Academic Article uri icon

abstract

  • Abstract Let β:= σ 1 σ 2− 1 be a braid in B 3, where B 3 is the braid group on 3 strings and σ 1, σ 2 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 β n is algebraically slice if and only if n is odd. As a consequence, we deduce some properties of Lucas numbers.

publication date

  • January 1, 2016