The pretzel knot P(4, -3, 5) is not squeezed

2025/11/05 by Nobuo Iida, Iida, Nobuo, Tatsumasa Suzuki +1
Mathematics · #57K10 #57K18 #57K41 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2511.03224

openalex publication_date 2025/11/05 · openalex created_date 2025/11/07 · openalex updated_date 2026/07/28

Abstract

We prove that an infinite family of three-strand pretzel knots is not squeezed. In particular, we show that P(4, -3, 5) is not squeezed. This answers a question posed by Lewark (2024). Our proof is obtained by comparing the Rasmussen invariant with the q_M-invariant introduced by Iida and Taniguchi.

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