Fredholm-Lagrangian-Grassmannian and the Maslov index

By Kenro Furutani. 2003

76 citations recorded by the source corpus.

Abstract This is a review article on the topology of the space, so called, Fredholm–Lagrangian–Grassmannian and the quantity “ Maslov index ” for paths in this space based on the standard theory of functional analysis. Our standing point is to define the Maslov index for arbitrary paths in terms of the fundamental spectral property of the Fredholm operators as an intersection number with the “Maslov cycle”. This argument was first recognized by J. Phillips and was used to define the “ Spectral flow ” not only for loops but also for arbitrary paths of selfadjoint Fredholm operators. We make the arguments as elementary as possible.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0026bfe5c9d7643adae2756c5c151c638e4ab341

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In Algebra and Number Theory

1. Jian Deng
2. Christopher Jones

In Applied Mathematics

1. Jian Deng
2. Christopher Jones

In Mathematical Physics

1. Jian Deng
2. Christopher Jones

Citations in the corpus

• MULTI-DIMENSIONAL MORSE INDEX THEOREMS AND A SYMPLECTIC VIEW OF ELLIPTIC BOUNDARY VALUE PROBLEMS (2011, methodology): “It can be shown that Λ(H) is an infinite dimensional differentiable manifold modeled on the Banach space of bounded selfadjoint operators [14].”