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Simple lift of non-simple closed curves
[Submitted on 11 Apr 2024 (v1), last revised 16 Jun 2026 (this v · 2026-06-17 · via math updates on arXiv.org

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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 $S$.

Submission history

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)