Links all of whose cyclic branched covers are L-spaces

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 $n\ge 1$. In addition, we show that the knots $K_k$ with $k\ge 1$ 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.

14 pages, 16 figures. Comments welcome!

References in corpus (3)

• On L-spaces and non left-orderable 3-manifold groups
• Slice and Gordian numbers of track knots
• Residual Torsion-Free Nilpotence, Bi-Orderability and Pretzel Knots

Cited by in corpus (3)

• Fixed-point-free pseudo-Anosov homeomorphisms, knot Floer homology and the cinquefoil
• Residual Torsion-Free Nilpotence, Bi-Orderability and Pretzel Knots
• Non-left-orderability of cyclic branched covers of pretzel knots $P(3,-3,-2k-1)$