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

TL;DR

This paper proves that the specific pretzel knot P(4, -3, 5) and an infinite family of similar knots are not squeezed, answering a question by Lewark through invariants comparison.

Contribution

It introduces a novel method comparing Rasmussen and q_M-invariants to determine the non-squeezed property of certain pretzel knots.

Findings

P(4, -3, 5) is not squeezed

An infinite family of three-strand pretzel knots are not squeezed

The method involves comparing Rasmussen and q_M-invariants

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.