What is a right-handed Dehn twist of a cut curve of a Riemann surface?

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 $\Sigma_g$?

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Please see the primer on mapping class groups. math.utah.edu/~margalit/primer –  Sam Nead Jun 24 '10 at 12:30