 Dehn twist

A Dehn twist $T_{\gamma }$ cuts an oriented surface along a simple closed curve $\gamma$, rotates one side once, and glues it back. If a curve or arc $\alpha$ has nonzero geometric intersection with $\gamma$, the iterates $T_{\gamma }^n(\alpha )$ usually represent distinct isotopy classes, with intersection numbers growing linearly in $|n|$.

A Dehn twist is a fundamental concept in the field of topology, particularly in the study of surfaces and 3-manifolds. It is a type of homeomorphism that can be used to analyze the properties of surfaces and their mappings.