Non-slice 3-stranded pretzel knots
Min Hoon Kim, Changhee Lee, Minkyoung Song

TL;DR
This paper investigates the sliceness of certain 3-stranded pretzel knots, showing that most in a specific family are not slice, thus contributing to the understanding of the slice-ribbon conjecture for these knots.
Contribution
It extends previous work by proving that four-fifths of the remaining family of pretzel knots are not slice, advancing the classification of these knots.
Findings
Most of the remaining family are not slice
Confirmed non-sliceness for a large subset of the family
Progress towards the slice-ribbon conjecture for pretzel knots
Abstract
Greene-Jabuka and Lecuona confirmed the slice-ribbon conjecture for 3-stranded pretzel knots except for an infinite family where is an odd integer greater than . Lecuona and Miller showed that are not slice unless . In this note, we show that four-fifths of the remaining knots in the family are not slice.
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Taxonomy
TopicsGeometric and Algebraic Topology · semigroups and automata theory · Advanced Combinatorial Mathematics
