$n$-Fold Cyclic Branched Covers and Overtwisted Contact Structures

Jose Ceniceros

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arXiv · 2308.05703

$n$-Fold Cyclic Branched Covers and Overtwisted Contact Structures

Jose Ceniceros

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Abstract

This article presents an alternate way to prove a result originally proven by Harvey, Kawamuro, and Plamenvskaya in \cite{HaKaPl}. We accomplish this by explicitly constructing an overtwisted disk in the $p$-fold cyclic branched cover of $S^3$ with the standard contact structure branched along a carefully selected transverse knot. Furthermore, by utilizing this construction of the overtwisted disk, we can see that the overtwisted disk is contained in the complement of the branch locus.

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Jose Ceniceros. 2023-08-10. $n$-Fold Cyclic Branched Covers and Overtwisted Contact Structures. https://arxiv.org/abs/2308.05703

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