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Lifts of simple curves in finite regular coverings of closed surfaces
Published 19 Aug 2015 in math.GT | (1508.04815v8)
Abstract: Suppose $S$ is a closed orientable surface and $\tilde{S}$ is a finite sheeted regular cover of $S$. The following question was posed by Juli\'{e}n March\'{e} in Mathoverflow: Do the lifts of simple curves from $S$ generate $H_{1}(\tilde{S},\mathbb{Z})$? A family of examples is given for which the answer is "no".
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