$n$-Fold Cyclic Branched Covers and Overtwisted Contact Structures
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909207974903808 |
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| author | Ceniceros, Jose |
| author_facet | Ceniceros, Jose |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05703 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $n$-Fold Cyclic Branched Covers and Overtwisted Contact Structures Ceniceros, Jose Geometric Topology Differential Geometry 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. |
| title | $n$-Fold Cyclic Branched Covers and Overtwisted Contact Structures |
| topic | Geometric Topology Differential Geometry |
| url | https://arxiv.org/abs/2308.05703 |