Links all of whose cyclic branched covers are L-spaces

Ahmad Issa; Hannah Turner

doi:10.1112/blms.12950

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arXiv · 2008.06127

Links all of whose cyclic branched covers are L-spaces

Ahmad Issa·Hannah Turner

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Abstract

We show that for the pretzel knots $K_k=P(3,-3,-2k-1)$, the $n$-fold cyclic branched covers are L-spaces for all $n\geq 1$. In addition, we show that the knots $K_k$ with $k\geq 1$ are quasipositive 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.

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Ahmad Issa, Hannah Turner. 2020-08-13. Links all of whose cyclic branched covers are L-spaces. https://doi.org/10.1112/blms.12950

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