Microlocal condition for non-displaceablility

TL;DR

This paper establishes a microlocal condition based on sheaf theory that guarantees non-displaceability of certain subsets in cotangent bundles, with applications to real projective space and Clifford torus.

Contribution

It introduces a new microlocal criterion for non-displaceability using sheaf-theoretic methods, advancing symplectic topology techniques.

Findings

Real projective space and Clifford torus are mutually non-displaceable.

The condition provides a new tool for symplectic non-displaceability proofs.

The approach links microlocal sheaf theory with symplectic geometry.

Abstract

We formulate a sufficient condition for non-displaceability (by Hamiltonian symplectomorphisms which are identity outside of a compact) of a pair of subsets in a cotangent bundle. This condition is based on micro-local analysis of sheaves on manifolds by Kashiwara-Schapira. This condition is used to prove that the real projective space and the Clifford torus inside the complex projective space are mutually non-displaceable