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arXiv · 0901.2563

Localization formulae in odd K-theory

Daniel Cibotaru
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Abstract

We describe a class of real Banach manifolds, which classify $K^{-1}$. These manifolds are Grassmannians of (hermitian) lagrangian subspaces in a complex Hilbert space. Certain finite codimensional real subvarieties described by incidence relations define geometric representatives for the generators of the cohomology rings of these classifying spaces. Any family of self-adjoint, Fredholm operators parametrized by a closed manifold comes with a map to one of these spaces. We use these Schubert varieties to describe the Poincare duals of the pull-backs to the parameter space of the cohomology ring generators. The class corresponding to the first generator is the spectral flow.

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Daniel Cibotaru. 2009-03-23. Localization formulae in odd K-theory. https://arxiv.org/abs/0901.2563

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