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arXiv · 2201.10616

Interior Kasparov product for $\varrho$-classes on Riemannian foliated bundles

Vito Felice Zenobi
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Abstract

Let $\iota\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 $(\iota_{ad}^{[0,1)})_!\in E_n\left(C^*(G_{ad}^{[0,1)}), C^*(H_{ad}^{[0,1)})\right)$, 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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Vito Felice Zenobi. 2022-01-25. Interior Kasparov product for $\varrho$-classes on Riemannian foliated bundles. https://doi.org/10.1016/j.jfa.2023.109863

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