Additional cases of positive twisted torus knots
| Autor: | Brandy Guntel Doleshal, Matt Rathbun, Evan Amoranto |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Algebra and Number Theory 010102 general mathematics Fibered knot Geometric Topology (math.GT) Torus 01 natural sciences Mathematics::Geometric Topology Torus knot Mathematics - Geometric Topology Knot (unit) 0103 physical sciences 57M25 57M27 FOS: Mathematics Braid 010307 mathematical physics 0101 mathematics Mathematics::Symplectic Geometry Mathematics |
| Popis: | A twisted torus knot is a knot obtained from a torus knot by twisting adjacent strands by full twists. The twisted torus knots lie in $F$, the genus 2 Heegaard surface for $S^3$. Primitive/primitive and primitive/Seifert knots lie in $F$ in a particular way. Dean gives sufficient conditions for the parameters of the twisted torus knots to ensure they are primitive/primitive or primitive/Seifert. Using Dean's conditions, Doleshal shows that there are infinitely many twisted torus knots that are fibered and that there are twisted torus knots with distinct primitive/Seifert representatives with the same slope in $F$. In this paper, we extend Doleshal's results to show there is a four parameter family of positive twisted torus knots. Additionally, we provide new examples of twisted torus knots with distinct representatives with the same surface slope in $F$. 22 pages, 18 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|