Let $\Sigma\_g$ be a Riemann surface of genus g, and $C$ is a cut curve of $\Sigma\_g$, i.e. an oriented simple close curve. 


What is a right-handed Dehn twist of $C$ of $\Sigma\_g$? 



What is a right-handed Dehn twist of a cut curve of a Riemann surface?
Cut the curve with a scalpel, going along the curve (it is oriented), rotate the right side 360 degrees, and glue it back in...


