Laura Starkson (Stanford University), Triangle Topology Seminar

Title:  Manipulating singularities of Weinstein skeleta

Abstract: Weinstein manifolds are an important class of symplectic manifolds with convex ends/boundary. These 2n dimensional manifolds come with a retraction onto a core n-dimensional stratified complex called the skeleton, which generally has singularities. The topology of the skeleton does not generally determine the smooth or symplectic structure of the 2n dimensional Weinstein manifold. However, if the singularities fall into a simple enough class (Nadler’s arboreal singularities), the whole Weinstein manifold can be recovered just from the data of the n-dimensional complex. We discuss work in progress showing that every Weinstein manifold can be homotoped to have a skeleton with only arboreal singularities (focusing in low-dimensions). Then we will discuss some of the expectations and hopes for what might be done with these ideas in the future.