= Monodromy permutation
{title2=$\rho(\gamma)\in\operatorname{Sym}(p^{-1}(x_0))$}
Lifting a based loop in a <covering space> from every point of its finite fibre gives a permutation of that fibre. Composition of lifted loops yields the <monodromy action of a covering space>. If a closed <geodesic> of length $\ell$ has a cycle of length $m$ in its <monodromy permutation>, the corresponding lift closes after $m$ traversals and has length $m\ell$. For a primitive base <geodesic>, these cycles describe the primitive lift components.
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