Infinite dimensional Grassmannians

Details Infinite dimensional Grassmannians Infinite dimensional Grassmannians

2003-07-14

arxiv.org/abs/math/0307192v2

Journal of Operator Theory 61 (2009), 16-62

Mathematics

Algebraic Topology

35 pages. Final version. Part on determinant bundles expanded

Scientific paper

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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