The adiabatic groupoid and the Higson–Roe exact sequence
| Autor: | Vito Felice Zenobi |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Exact sequence Algebra and Number Theory Discrete group Riemannian manifold K-theory Coarse geometry secondary invariants Lie groupoid Mathematics::K-Theory and Homology Surgery exact sequence Lie groupoids Mathematics::Differential Geometry Geometry and Topology Isomorphism Mathematical Physics Mathematics Scalar curvature |
| Zdroj: | Journal of Noncommutative Geometry. 15:797-827 |
| ISSN: | 1661-6952 |
| DOI: | 10.4171/jncg/422 |
| Popis: | Let $\widetilde{X}$ be a smooth Riemannian manifold equipped with a proper, free, isometric and cocompact action of a discrete group $\Gamma$. In this paper we prove that the analytic surgery exact sequence of Higson-Roe for $\widetilde{X}$ is isomorphic to the exact sequence associated to the adiabatic deformation of the Lie groupoid $\widetilde{X}\times_\Gamma\widetilde{X}$. We then generalize this result to the context of smoothly stratified manifolds. Finally, we show, by means of the aforementioned isomorphism, that the $\varrho$-classes associated to a metric with positive scalar curvature defined by Piazza and Schick corresponds to the $\varrho$-classes defined by the author of this paper. |
| Databáze: | OpenAIRE |
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