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arXiv · 2204.04133

On the supports in the Humilière completion and $γ$-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 $γ$-support. We also define the notion of $γ$-coisotropic set, and prove that a $γ$-support must be $γ$-coisotropic toghether with many properties of the $γ$-support and $γ$-coisotropic sets. We give examples of Lagrangians in the completion having large $γ$-support and we study those (called "regular Lagrangians") having small $γ$-support. We compare the notion of $γ$-coisotropy with other notions of isotropy.

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Claude Viterbo. 2026-03-17. On the supports in the Humilière completion and $γ$-coisotropic sets. https://arxiv.org/abs/2204.04133

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