November 9, 2025Open Access

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

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The knot P(4, -3, 5) is proven to be not squeezed, expanding on earlier work in knot theory.
The findings contribute to understanding specific properties of three-strand pretzel knots and their invariants.
A comparison of two invariants, the Rasmussen invariant and the q_M-invariant, underpins the proof of non-squeezability.
This insight may influence future research in knot theory and related mathematical fields.

Implication

Proof shows P(4, -3, 5) is not squeezed, indicating broader implications for three-strand pretzel knots.

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 qM-invariant introduced by Iida and Taniguchi.

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Cite This Study

Iida et al. (2025) studied this question.

synapsesocial.com/papers/690fdcdaf60c54d04ea38128 https://doi.org/10.48550/arxiv.2511.03224

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Implication

Proof shows P(4, -3, 5) is not squeezed, indicating broader implications for three-strand pretzel knots.

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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