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This is a Quantitative Study study.

September 30, 2025Open Access

The knot quandles of Suciu's ribbon n-knots and automorphisms on the free group of rank two

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The study finds that Suciu's $n$-knots have mutually non-isomorphic knot quandles, confirming previous results.
Key evidence includes the analysis of automorphisms in the context of free groups, underpinning the theorem's validity.
This analysis employed conjugacy classes, providing a novel perspective on understanding the properties of ribbon $n$-knots.
These findings underscore the complexity of knot theory, particularly in how knot quandles relate to group isomorphism.

Implication

Different approaches confirm that Suciu's $n$-knots exhibit non-isomorphic knot quandles, revealing insights into automorphisms.

Abstract

Jabłonowski proved that the knot quandles of Suciu's n-knots, which share isomorphic knot groups, are mutually non-isomorphic, and Yasuda later gave a different proof. In this paper, we present yet another proof of this result by analyzing the conjugacy classes of certain automorphisms of the free group of rank two.

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Cite This Study

Sakasai et al. (2025) studied this question.

synapsesocial.com/papers/68dc12cc8a7d58c25ebb0e44 https://doi.org/10.48550/arxiv.2509.07395

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Implication

Different approaches confirm that Suciu's $n$-knots exhibit non-isomorphic knot quandles, revealing insights into automorphisms.

The knot quandles of Suciu's ribbon n-knots and automorphisms on the free group of rank two

Key Points

Implication

Abstract

Discussion

Cite This Study

The knot quandles of Suciu's ribbon n-knots and automorphisms on the free group of rank two

Key Points

Implication

Abstract

Discussion

Cite This Study

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