Unlike Riemannian geometry, symplectic geometry is a soft theory in that it does not admit any local invariants such as curvature. Detecting global invariants is thus an important question for the theory. Instead of the more standard method of pseudo-holomorphic disks, I will discuss a topological/algebraic approach using microlocal sheaf theory. In particular, the wrapped Fukaya category, a version of Fukaya category for open symplectic manifolds, admits a purely sheaf theoretic description. I will explain this equivalence with a concrete example and, if time permits, present a new sheaf theoretic construction which has features resembling the Fukaya ones.

 

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