Morse Theory, Sheaves, and Locally Conformally Symplectic Geometry

Locally conformally symplectic (LCS) manifolds are manifolds that are symplectic up to a locally defined positive factor. In this generalization, we still have (locally conformally) exact Lagrangians, (locally conformally) Hamiltonian vector fields, etc. Moreover, generalizing local properties from symplectic manifolds to LCS manifolds is also straightforward. For example, there is an LCS version of the Weinstein neighborhood theorem, Moser's trick, and so on. However, we currently lack the tools to systematically generalize rigidity properties (e.g. the Arnold conjecture).

In this talk, we will see how we can leverage insights from Morse theory to prove an LCS version of the Arnold conjecture on cotangent bundles using derived sheaves.