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

2017/12/31 by Tomohiro Asano, Yuichi Ike · 1 citation
Mathematics · #math.SG #math.AT #msc:37J10 #msc:53D35 #msc:55U99 #msc:35A27

paper · pdf · doi:10.4310/jsg.2020.v18.n3.a1

published as J. Symp. Geom. 18:3 (2020) 613-649 · 27 pages, 2 figures, v3: final version, v2: revised

arxiv created 2020/08/04 · arxiv updated 2020/08/06

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.

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