Primitive closed geodesic
= Primitive closed geodesic
{title2=$\gamma\ne\eta^m\quad(m\geq2)$}
A <primitive closed geodesic> is a closed <geodesic> with its smallest positive period, rather than a repeated traversal of a shorter periodic geodesic. A degree-$m$ lift of a primitive base geodesic is still primitive upstairs when its <monodromy permutation> has a cycle of exact length $m$: no smaller number of traversals returns to the starting sheet.