= Fenchel–Nielsen twist
{c}
{title2=$\tau$}
After cutting a <hyperbolic surface> along a simple closed <geodesic>, reglue its two boundary copies after an arclength displacement $\tau$. The boundary length remains fixed, while the <Riemannian metric> varies. In marked <Fenchel–Nielsen coordinates>, the twist is real-valued; changing it by one boundary length corresponds to a <Dehn twist> in the marking. This construction also applies to a hyperbolic pair of pants with a fixed cone angle and two geodesic boundaries.
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