Abstract
Greene-Jabuka and Lecuona confirmed the slice-ribbon conjecture for 3-stranded pretzel knots except for an infinite family P(a,-a - 2,-(a+1)2 2), where a is an odd integer greater than 1. Lecuona and Miller showed that P(a,-a - 2,-(a+1)2 2) are not slice unless a 1, 11, 37, 47, 59(mod 60). In this note, we show that four-fifths of the remaining knots in the family are not slice.
| Original language | English |
|---|---|
| Article number | 2250018 |
| Journal | Journal of Knot Theory and its Ramifications |
| Volume | 31 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1 Mar 2022 |
Bibliographical note
Publisher Copyright:© 2022 World Scientific Publishing Company.
Keywords
- irreducible polynomials
- pretzel knots
- Slice-ribbon conjecture