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arXiv · 1901.05081

The adiabatic groupoid and the Higson-Roe exact sequence

Vito Felice Zenobi
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Abstract

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.

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Vito Felice Zenobi. 2019-01-15. The adiabatic groupoid and the Higson-Roe exact sequence. https://arxiv.org/abs/1901.05081

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