Full Lutz twist along the binding of an open book

Abstract

Let $T$ denote a binding component of an open book $(\Sigma ,\varphi )$ compatible with a closed contact 3-manifold $(M,\xi )$. We describe an explicit open book $({\Sigma }^{\prime },{\varphi }^{\prime })$ compatible with $(M,\zeta )$, where $\zeta$ is the contact structure obtained from $\xi$ by performing a full Lutz twist along $T$. Here, $({\Sigma }^{\prime },{\varphi }^{\prime })$ is obtained from $(\Sigma ,\varphi )$ by a \emph{local} modification near the binding.

7 pages, 3 figures

References in corpus (2)

• A Legendrian surgery presentation of contact 3-manifolds
• On the transverse invariant for bindings of open books