Links all of whose cyclic‐branched covers are L‐spaces

We show that for the pretzel knots Kk=P(3,−3,−2k−1)$K_k=P(3,-3,-2k-1)$, the n$n$‐fold cyclic‐branched covers are L‐spaces for all n⩾1$n\geqslant 1$. In addition, we show that the knots Kk$K_k$ with k⩾1$k\geqslant 1$ are quasi‐positive and slice, answering a question of Boileau–Boyer–Gordon. We also...

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Bibliographic Details
Published in:The Bulletin of the London Mathematical Society 2024-02, Vol.56 (2), p.566-580
Main Authors: Issa, Ahmad, Turner, Hannah
Format: Article
Language:English
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Summary:We show that for the pretzel knots Kk=P(3,−3,−2k−1)$K_k=P(3,-3,-2k-1)$, the n$n$‐fold cyclic‐branched covers are L‐spaces for all n⩾1$n\geqslant 1$. In addition, we show that the knots Kk$K_k$ with k⩾1$k\geqslant 1$ are quasi‐positive and slice, answering a question of Boileau–Boyer–Gordon. We also extend results of Teragaito giving examples of two‐bridge knots with all L‐space cyclic‐branched covers to a family of two‐bridge links.
ISSN:0024-6093
1469-2120
DOI:10.1112/blms.12950