Simple lift of non-simple closed curves

Deblina Das; Arpan Kabiraj

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arXiv · 2404.07627

Simple lift of non-simple closed curves

Deblina Das·Arpan Kabiraj

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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 $S$.

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Deblina Das, Arpan Kabiraj. 2024-04-11. Simple lift of non-simple closed curves. https://arxiv.org/abs/2404.07627

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