Full Lutz twist along the binding of an open book

Abstract

Let $T$ denote a binding component of an open book $(\Sigma, \phi)$ compatible with a closed contact 3-manifold $(M, \xi)$. We describe an explicit open book $(\Sigma', \phi')$ compatible with $(M, \zeta)$, where $\zeta$ is the contact structure obtained from $\xi$ by performing a full Lutz twist along $T$. Here, $(\Sigma', \phi')$ is obtained from $(\Sigma, \phi)$ by a \emph{local} modification near the binding.