Joint IAS/Princeton University Symplectic Geometry Seminar

We will discuss how to study the symplectic geometry of $2n$-dimensional Weinstein manifolds via the topology of a core $n$-dimensional complex called the skeleton. We show that the Weinstein structure can be homotoped to admit a skeleton with a unique symplectic neighborhood. Then we further work to reduce the remaining singularities to a simple combinatorial list coinciding with Nadler's arboreal singularities. We will discuss how arboreal singularities occur naturally in a Weinstein skeleton, and what information about the symplectic manifold one might hope to extract out of an arboreal complex.