Heavy subsets from microsupports

TL;DR

This paper introduces a method to construct partial symplectic quasi-states on cotangent bundles using microlocal sheaf theory, providing criteria for heaviness and superheaviness relative to these states.

Contribution

It presents a novel construction of partial symplectic quasi-states via microlocal sheaf theory and characterizes heaviness and superheaviness in this context.

Findings

Constructed partial symplectic quasi-states on cotangent bundles.

Provided criteria for heaviness and superheaviness.

Linked microlocal sheaf theory with symplectic topology.

Abstract

We construct partial symplectic quasi-states on a cotangent bundle with the use of microlocal sheaf theory. We also give criteria and characterization for heaviness/superheaviness with respect to the partial symplectic quasi-state.