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arXiv · 1601.03992

Signatures for $J$-hermitians and $J$-unitaries on Krein spaces with Real structures

Hermann Schulz-Baldes·Carlos Villegas-Blas
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Abstract

For $J$-hermitian operators on a Krein space $(\mathcal{K},J)$ satisfying an adequate Fredholm property, a global Krein signature is shown to be a homotopy invariant. It is argued that this global signature is a generalization of the Noether index. When the Krein space has a supplementary Real structure, the sets of $J$-hermitian Fredholm operators with Real symmetry can be retracted to certain of the classifying spaces of Atiyah and Singer. Secondary $\mathbb{Z}_2$-invariants are introduced to label their connected components. Related invariants are also analyzed for $J$-unitary operators.

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Hermann Schulz-Baldes, Carlos Villegas-Blas. 2016-01-15. Signatures for $J$-hermitians and $J$-unitaries on Krein spaces with Real structures. https://arxiv.org/abs/1601.03992

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