Ana Rechtman (Université Grenoble Alpes)
Abstract: Every non degenerate Reeb vector field on a closed 3-manifold is carried by a broken book decomposition. A broken book provides a system of transverses surfaces to the flow that allow to code the dynamics, allowing to prove several generic properties of Reeb vector fields. In particular, it allows to construct a Birkhoff section or, equivalently, a compatible open book decomposition (under generic hypothesis). After explaining these results, I will present results that can be obtained for generic Reeb vector fields in dimension 3. This is work in collaboration with V. Colin, P. Dehornoy and U. Hryniewicz.