Persistence-like distance on Tamarkin's category and symplectic displacement energy

TL;DR

This paper introduces a new pseudo-distance in Tamarkin's category, linking it to Hamiltonian deformations and providing quantitative bounds on symplectic displacement energy, advancing understanding in symplectic topology.

Contribution

It defines a persistence-like pseudo-distance in Tamarkin's category and establishes its relation to Hamiltonian deformation and displacement energy bounds.

Findings

Distance between an object and its Hamiltonian deformation is bounded by the Hofer norm.

Provides a quantitative version of Tamarkin's non-displaceability theorem.

Establishes lower bounds for displacement energy of compact subsets in cotangent bundles.

Abstract

We introduce a persistence-like pseudo-distance on Tamarkin's category and prove that the distance between an object and its Hamiltonian deformation is at most the Hofer norm of the Hamiltonian function. Using the distance, we show a quantitative version of Tamarkin's non-displaceability theorem, which gives a lower bound of the displacement energy of compact subsets of cotangent bundles.