Cyclic branched covers of alternating knots and $L$-spaces
Bull. Korean Math. Soc. 2015 Vol. 52, No. 4, 1139-1148
https://doi.org/10.4134/BKMS.2015.52.4.1139
Published online July 31, 2015
Masakazu Teragaito
Hiroshima University
Abstract : For any alternating knot, it is known that the double branch\-ed cover of the $3$-sphere branched over the knot is an $L$-space. We show that the three-fold cyclic branched cover is also an $L$-space for any genus one alternating knot.
Keywords : branched cover, alternating knot, pretzel knot, $L$-space
MSC numbers : Primary 57M25
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