Persistence-like distance on Tamarkin's category and symplectic displacement energy
Symplectic Geometry
2020-08-06 v3 Algebraic Topology
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.
Keywords
Cite
@article{arxiv.1712.06847,
title = {Persistence-like distance on Tamarkin's category and symplectic displacement energy},
author = {Tomohiro Asano and Yuichi Ike},
journal= {arXiv preprint arXiv:1712.06847},
year = {2020}
}
Comments
27 pages, 2 figures, v3: final version, v2: revised