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$2$-knots with the same knot group but different knot quandles

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arxiv 2308.07782 v1 pith:YUQ7DQ45 submitted 2023-08-15 math.GT

Kokoro Tanaka , Yuta Taniguchi This is my paper · ORCID
classification math.GT
keywords knotquandlesdifferentgivegroupknotssamespins
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We give a first example of 2-knots with the same knot group but different knot quandles by analyzing the knot quandles of twist spins. As a byproduct of the analysis, we also give a classification of all twist spins with finite knot quandles.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Characterizations of knot groups and knot symmetric quandles of surface-links

    math.GT 2024-12 conditional novelty 6.0 of 10

    A group is the knot group of a surface-link, orientable or not, exactly when it admits a (2m,n)-presentation with inverses satisfying the weak ∂-condition, and an analogous statement holds for knot symmetric quandles.

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

    math.GT 2025-09 accept novelty 5.0 of 10

    Suciu's ribbon n-knots are mutually distinguished by knot quandles, reproved by showing their associated free-group automorphisms are non-conjugate.

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