Infinite dimensional Grassmannians
classification
🧮 math.AT
math.OA
keywords
dimensionalinfinitespacegrassmannianshomotopyanalyticbundleclosed
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We study the analytic and homotopy properties of some infinite dimensional Grassmannians, useful for developing a Morse theory for infinite dimensional manifolds. We study the space of Fredholm pairs of a Hilbert space, we determine its homotopy type, and we define a determinant bundle over it. We study the space of compact perturbations of a given closed linear subspace, and the related concept of essential Grassmannian.
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