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

Tomohiro Asano; Yuichi Ike

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

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arxiv 1712.06847 v3 pith:JVOT3TWZ submitted 2017-12-19 math.SG math.AT

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

Tomohiro Asano , Yuichi Ike This is my paper

classification math.SG math.AT

keywords distancetamarkincategorydisplacementenergyhamiltonianpersistence-likebound

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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.

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

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