2021/01/04 by Min Hoon Kim, Changhee Lee, Kim, Min Hoon +3
Computer Science · Mathematics · #57K10 #57K31 #57K40 #57N70 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2101.00865
openalex publication_date 2021/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \pmod60. In this note, we show that four-fifths of the remaining knots in the family are not slice.