Simple lift of non-simple closed curves
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909218031796224 |
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| author | Das, Deblina Kabiraj, Arpan |
| author_facet | Das, Deblina Kabiraj, Arpan |
| contents | Given a compact, oriented surface $S$ of finite genus and finitely many boundary components, we provide examples of finite covers $\tilde{S}$ of $S$ and non-simple closed curves $γ$ on $S$ which lifts to simple closed curves on $\tilde{S}$. In particular, given any positive integer $n\geq 2$, we construct explicit non-simple closed curves on $S$ which has a simple lift to a degree $n$ cover of $S$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07627 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simple lift of non-simple closed curves Das, Deblina Kabiraj, Arpan Geometric Topology M57M07 Given a compact, oriented surface $S$ of finite genus and finitely many boundary components, we provide examples of finite covers $\tilde{S}$ of $S$ and non-simple closed curves $γ$ on $S$ which lifts to simple closed curves on $\tilde{S}$. In particular, given any positive integer $n\geq 2$, we construct explicit non-simple closed curves on $S$ which has a simple lift to a degree $n$ cover of $S$. |
| title | Simple lift of non-simple closed curves |
| topic | Geometric Topology M57M07 |
| url | https://arxiv.org/abs/2404.07627 |