ScalingStacks

Definition 7.2.1. We define a curve to be a $1$-dimensional space $Z$ endowed with

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  an open subset $Z_{o}$ containing $Z_{exc}$

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  an orientation of $Z_{o}-Z_{exc}$ and

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  a fixed-point free involution $\iota$ of $C_{Z}(z)$ for every $z\in Z_{exc}$

satisfying the following conditions:

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  $\partial Z=\emptyset$

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  $Z-Z_{o}$ has finitely many connected components, none of which are points

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  given $z\in Z_{exc}$, given $U$ a small open neighbourhood of $z$ in $Z_{o}$, and given $L\in\pi_{0}(U-\{z\})$, then $L\cup\iota(L)\cup\{z\}$ has an orientation extending the given orientations on $L$ and $\iota(L)$.