A topological Maslov index for 3-graded lie groups

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Abstract

Motivated by the generalization of the Maslov index to tube domains and by numerous applications of related index function in infinite-dimensional situations, we describe in this paper a topologically oriented approach to an index function generalizing the Maslov index for bounded symmetric domains of tube type to a variety of infinite-dimensional situations containing in particular the class of all bounded symmetric domains of tube type in Banach spaces. The framework is that of 3-graded Banach–Lie groups and corresponding Jordan triple systems.

Keywords

Maslov index
Bounded symmetric domains
Banach Jordan algebras

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