黎曼叶状丛上$\varrho$类的内Kasparov积
Interior Kasparov product for $\varrho$-classes on Riemannian foliated bundles
摘要：
设$ι\colon \mathcal{F}_0\to\mathcal{F}_1 $是流形$M$上的叶理的适当定向包含，将Hilsum和Skandalis给出的下shriek映射的构造推广到绝热变形广群C*-代数：构造了一个渐近态射$(ι_{ad}^{[0,1)})_!\in E_n\left(C^*(G_{ad}^{[0,1)}), C^*(H_{ad}^{[0,1)})\right)$，其中$G$和$H$分别是与$\mathcal{F}_0$和$\mathcal{F}_1$相关的单值广群.此外，我们证明了一个内部卡斯帕罗夫积公式的叶状$\varrho$类与纵向度量的正数量曲率的情况下，黎曼叶状丛。
英文摘要：
Let $ι\colon \mathcal{F}_0\to\mathcal{F}_1 $ be a suitably oriented inclusion of foliations over a manifold $M$, then we extend the construction of the lower shriek maps given by Hilsum and Skandalis to adiabatic deformation groupoid C*-algebras: we construct an asymptotic morphism $(ι_{ad}^{[0,1)})_!\in E_n\left(C^*(G_{ad}^{[0,1)}), C^*(H_{ad}^{[0,1)})\right)$, where $G$ and $H$ are the monodromy groupoids associated with $\mathcal{F}_0$ and $\mathcal{F}_1$ respectively. Furthermore, we prove an interior Kasparov product formula for foliated $\varrho$-classes associated with longitudinal metrics of positive scalar curvature in the case of Riemannian foliated bundles.
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