Journal of Symplectic Geometry

Volume 18 (2020)

Number 3

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

Pages: 613 – 649



Tomohiro Asano (Graduate School of Mathematical Sciences, University of Tokyo, Meguro-ku, Tokyo, Japan)

Yuichi Ike (Fujitsu Laboratories Ltd., Nakahara-ku, Kawasaki, Kanagawa, Japan)


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.

Received 19 March 2018

Accepted 16 July 2019

Published 30 July 2020