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arXiv · 2410.06930

The Spectral Flow of a Restriction to a Subspace and the Maslov Indices in a Symplectic Reduction

Henrique Vitório
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Abstract

We give a simple proof of a known 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.

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Henrique Vitório. 2024-10-09. The Spectral Flow of a Restriction to a Subspace and the Maslov Indices in a Symplectic Reduction. https://arxiv.org/abs/2410.06930

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