Simple closed curves in stable covers of surfaces

Nick Salter

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arXiv · 2109.13310

Simple closed curves in stable covers of surfaces

Nick Salter

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Abstract

Let $f: X \to Y$ be a regular covering of a surface $Y$ of finite type with nonempty boundary, with finitely-generated (possibly infinite) deck group $G$. We give necessary and sufficient conditions for an integral homology class on $X$ to admit a representative as a connected component of the preimage of a nonseparating simple closed curve on $Y$, possibly after passing to a "stabilization", i.e. a $G$-equivariant embedding of covering spaces $X \hookrightarrow X^+$.

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Nick Salter. 2021-09-27. Simple closed curves in stable covers of surfaces. https://arxiv.org/abs/2109.13310

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