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arXiv · 1712.06847

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

Tomohiro Asano·Yuichi Ike
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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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Tomohiro Asano, Yuichi Ike. 2017-12-19. Persistence-like distance on Tamarkin's category and symplectic displacement energy. https://doi.org/10.4310/jsg.2020.v18.n3.a1

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