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

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.

27 pages, 2 figures, v3: final version, v2: revised

Cited by in corpus (6)

• Ephemeral persistence modules and distance comparison
• Wrapped sheaves
• Sheaf quantization and intersection of rational Lagrangian immersions
• The $\gamma$-support as a micro-support
• Completeness of derived interleaving distances and sheaf quantization of non-smooth objects
• Lagrangian cobordism and shadow distance in Tamarkin category