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arXiv · 2204.04133

On the supports in the Humili\`ere completion and $\gamma$-coisotropic sets

Claude Viterbo
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Abstract

The symplectic spectral metric on the set of Lagrangian submanifolds or Hamiltonian maps can be used to define a completion of these spaces. For an element of such a completion, we define its $\gamma$-support. We also define the notion of $\gamma$-coisotropic set, and prove that a $\gamma$-support must be $\gamma$-coisotropic toghether with many properties of the $\gamma$-support and $\gamma$-coisotropic sets. We give examples of Lagrangians in the completion having large $\gamma$-support and we study those (called "regular Lagrangians") having small $\gamma$-support. We compare the notion of $\gamma$-coisotropy with other notions of isotropy.

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Claude Viterbo. 2022-04-08. On the supports in the Humili\`ere completion and $\gamma$-coisotropic sets. https://arxiv.org/abs/2204.04133

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