The Spectral Flow of a Restriction to a Subspace and the Maslov Indices in a Symplectic Reduction
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929620381597696 |
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| author | Vitório, Henrique |
| author_facet | Vitório, Henrique |
| contents | We prove in full generality a formula that relates the spectral flow of a continuous path of quadratic forms of Fredholm type with the spectral flow of the restrictions of the forms to a fixed closed finite codimensional subspace. We then apply this to obtain a formula relating the Maslov index of a continuous path in a Fredholm Lagrangian Grassmannian with the Maslov index of its symplectic reduction by a closed finite codimensional coisotropic subspace. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06930 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Spectral Flow of a Restriction to a Subspace and the Maslov Indices in a Symplectic Reduction Vitório, Henrique Functional Analysis We prove in full generality a formula that relates the spectral flow of a continuous path of quadratic forms of Fredholm type with the spectral flow of the restrictions of the forms to a fixed closed finite codimensional subspace. We then apply this to obtain a formula relating the Maslov index of a continuous path in a Fredholm Lagrangian Grassmannian with the Maslov index of its symplectic reduction by a closed finite codimensional coisotropic subspace. |
| title | The Spectral Flow of a Restriction to a Subspace and the Maslov Indices in a Symplectic Reduction |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2410.06930 |