Abstract: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 $\gamma$ 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 $S$.
From: Deblina Das [view email]
[v1]
Thu, 11 Apr 2024 10:27:06 UTC (2,198 KB)
[v2]
Thu, 6 Jun 2024 05:38:48 UTC (2,199 KB)
[v3]
Tue, 16 Jun 2026 14:40:34 UTC (1,919 KB)
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