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Bull. Korean Math. Soc. 2015; 52(4): 1139-1148

Printed July 31, 2015

https://doi.org/10.4134/BKMS.2015.52.4.1139

Copyright © The Korean Mathematical Society.

Cyclic branched covers of alternating knots and $L$-spaces

Masakazu Teragaito

Hiroshima University

Abstract

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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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