Yuichi Ike, Kyushu University

Abstract: To a compact exact Lagrangian submanifold of a cotangent bundle, one can associate a sheaf on the product space of the base and the real line. The space of compact exact Lagrangians carries the spectral metric, and we can consider its completion. Recently, Viterbo associated a closed subset called γ-support to an element of the completion. In this talk, I will explain how we can use sheaf-theoretic methods to explore the completion and γ-supports. In particular, I would like to show that the correspondence from Lagrangians to sheaves extends to the completion, and the notions of γ-support and (reduced) microsupports coincide through the extended correspondence.

This is joint work with Asano, Guillermou, Humilière, and Viterbo.