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Persistence-like distance on Tamarkin’s category and symplectic displacement energy
Journal of Symplectic Geometry ( IF 0.6 ) Pub Date : 2020-01-01 , DOI: 10.4310/jsg.2020.v18.n3.a1
Tomohiro Asano 1 , Yuichi Ike 2
Affiliation  

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 in a cotangent bundle.

中文翻译:

Tamarkin 范畴上的类持久距离和辛位移能

我们在 Tamarkin 的范畴上引入了一个类似持久性的伪距离,并证明了一个物体与其哈密顿变形之间的距离至多是哈密顿函数的 Hofer 范数。使用距离,我们展示了 Tamarkin 不可位移定理的定量版本,它给出了余切丛中紧子集的位移能量的下界。
更新日期:2020-01-01
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