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arXiv · 1808.08464

The Maslov Index and the Spectral Flow - revisited

Marek Izydorek·Joanna Janczewska·Nils Waterstraat
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Abstract

We give an elementary proof of a celebrated theorem of Cappell, Lee and Miller which relates the Maslov index of a pair of paths of Lagrangian subspaces to the spectral flow of an associated path of selfadjoint first-order operators. We particularly pay attention to the continuity of the latter path of operators, where we consider the gap-metric on the set of all closed operators on a Hilbert space. Finally, we obtain from Cappell, Lee and Miller's theorem a spectral flow formula for linear Hamiltonian systems which generalises a recent result of Hu and Portaluri.

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Marek Izydorek, Joanna Janczewska, Nils Waterstraat. 2018-08-25. The Maslov Index and the Spectral Flow - revisited. https://arxiv.org/abs/1808.08464

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