Displaying similar documents to “Index theory for skew-adjoint Fredholm operators”

The geometry of Kato Grassmannians

Bogdan Bojarski, Giorgi Khimshiashvili (2005)

Open Mathematics

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We discuss Fredholm pairs of subspaces and associated Grassmannians in a Hilbert space. Relations between several existing definitions of Fredholm pairs are established as well as some basic geometric properties of the Kato Grassmannian. It is also shown that the so-called restricted Grassmannian can be endowed with a natural Fredholm structure making it into a Fredholm Hilbert manifold.

Systems of Inclusions Involving Fredholm Operators and Noncompact Maps

Dorota Gabor (2007)

Bollettino dell'Unione Matematica Italiana

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We consider the existence of solutions to the system of two inclusions involving Fredholm operators of nonnegative index and the so-called fundamentally restrictible maps with not necessarily convex values. We apply the technique of a solution map and, since the assumptions admit a 'dimension defect', we use the coincidence index, i.e. the homotopy invariant based on the cohomotopy theory. Two examples of applications to boundary value problems are included.

Self homotopy equivalences of classifying spaces of compact connected Lie groups

Stefan Jackowski, James McClure, Bob Oliver (1995)

Fundamenta Mathematicae

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We describe, for any compact connected Lie group G and any prime p, the monoid of self maps B G p → B G p which are rational equivalences. Here, B G p denotes the p-adic completion of the classifying space of G. Among other things, we show that two such maps are homotopic if and only if they induce the same homomorphism in rational cohomology, if and only if their restrictions to the classifying space of the maximal torus of G are homotopic.

On canonical homotopy operators for ∂ in Fock type spaces in C.

Jörgen Boo (2001)

Publicacions Matemàtiques

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We show that a certain solution operator for ∂ in a space of forms square integrable against e-|z|2 is canonical, i.e., that it gives the minimal solution when applied to a ∂-closed form, and gives zero when applied to a form orthogonal to Ker ∂. As an application, we construct a canonical homotopy operator for i∂∂.