GT seminar: "Homotopy rigidity of nearby Lagrangian cocores"

Abstract: An exact Lagrangian L in a Weinstein manifold X is called a nearby cocore if it is equal to a Hamiltonian pushoff of a Lagrangian cocore at infinity, and stays away from all Lagrangian cocores. I will discuss the result that the restriction to L of the composition of the projection to the skeleton of X and a certain quotient map, is null-homotopic if dim X > 3, generalizing earlier work by Ekholm–Smith. The proof uses Floer theory with coefficients in the spin cobordism spectrum, and along the way we show that any closed exact Lagrangian in a cotangent bundle is isomorphic to the zero section in the spectral Donaldson–Fukaya category with coefficients in any connective ring spectrum. We also describe a definition of the spectral wrapped Fukaya category without spectra. This reports on joint work in progress with Yash Deshmukh and Alex Pieloch.

This is a seminar in our Geometry and Topology seminar series.