University of Arkansas Topology Seminar: 4/20/2023

Speaker: Gabriel Islambouli

Title: Multisections with divides and Weinstein manifolds

We show how to encode a Weinstein 4−manifold by a sequence of cut systems on a surface, together with a dividing set of curves. This comes from a decomposition of the manifold into standard Weinstein 1−handlebodies which we call a multisection with divides. This decomposition induces a contact Heegaard splitting on the boundary, which can be viewed as the "double" of an open book supporting the induced contact structure on the boundary of the Weinstein manifold. We show how our construction very naturally arises when viewing the Weinstein manifold as a Lefschetz fibration (or more specifically a PALF). We also give an algorithm to pass from Weinstein handle decompositions to multisections with divides. This is joint work with Laura Starkston.