On the supports in the Humilière completion and $γ$-coisotropic sets
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866914402915057664 |
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| author | Viterbo, Claude |
| author_facet | Viterbo, Claude |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_04133 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the supports in the Humilière completion and $γ$-coisotropic sets Viterbo, Claude Symplectic Geometry Dynamical Systems 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. |
| title | On the supports in the Humilière completion and $γ$-coisotropic sets |
| topic | Symplectic Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2204.04133 |