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 |
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Pages (from-to) | 180-185 |
Number of pages | 6 |
Journal | Topology and its Applications |
Volume | 214 |
DOIs | |
State | Published - 1 Dec 2016 |
Keywords
- Braids
- Concordance
- Gauss diagrams
- Knots
ASJC Scopus subject areas
- Geometry and Topology