Persistence Homology in Symplectic and Contact Topology

Sheaves for the completion of the space of Lagrangians

12 juin 2023, 14:30

1h

Albi

Orateur

Stéphane Guillermou

Description

For a manifold $M$ it is known that we can associate a sheaf on $M\times \mathbb{R}$ to any exact Lagrangian submanifold of $T^{\ast }M$. The space of exact Lagrangians carries the Viterbo's metric and, following Humili`ere, we can consider its completion. We will see that the correspondence between sheaves and symplectic geometry extends to this framework and, moreover, natural notions defined for the objects on both sides coincide: to any element in the completion of the space of Lagrangians we can associate a sheaf; the notions of $\gamma$-support and microsupport coincide and the microsupport of any sheaf if $\gamma$-coisotropic.

These are joint works with Viterbo and Asano, Humilière, Ike, Viterbo.