奇K-理论中的局部化公式
Localization formulae in odd K-theory
摘要：
我们描述了一类实巴拿赫流形，它是$K^{-1}$的分类.这些流形是复希尔伯特空间中（厄米）拉格朗日子空间的格拉斯曼流形。由关联关系描述的某些有限余维实子簇定义了这些分类空间的上同调环的生成元的几何表示。任何由闭流形参数化的自伴弗雷德霍姆算子族都带有到这些空间之一的映射。我们用这些Schubert簇来描述拉回到上同调环生成元的参数空间的Poincare图。对应于第一个生成器的类是谱流。
英文摘要：
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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