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- W4387355814 abstract "We investigate a polynomial factorization problem which naturally arises in Hartley's factorization condition on the Alexander polynomial of freely periodic knots. We give a number-theoretic interpretation of this factorization condition, which allows for efficient computation. As an application, we prove that any polynomial which is not a product of cyclotomic polynomials can be the Alexander polynomial of a freely $p$-periodic knot for only finitely many $p$. As a demonstration of the computational efficiency of these methods, we also show that the Alexander polynomial of any freely-periodic L-space knot with genus at most 16 must be a product of cyclotomic polynomials. We conjecture that any periodic or freely periodic L-space knot must be an iterated torus knot." @default.
- W4387355814 created "2023-10-05" @default.
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- W4387355814 date "2023-10-02" @default.
- W4387355814 modified "2023-10-06" @default.
- W4387355814 title "Obstructions to free periodicity and symmetric L-space knots" @default.
- W4387355814 doi "https://doi.org/10.48550/arxiv.2310.01705" @default.
- W4387355814 hasPublicationYear "2023" @default.
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