The adiabatic groupoid and the Higson–Roe exact sequence
Vito Felice Zenobi
Sapienza Università di Roma, Italy
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Abstract
Let be a smooth Riemannian manifold equipped with a proper, free, isometric, and cocompact action of a discrete group . In this paper, we prove that the analytic surgery exact sequence of Higson–Roe for is isomorphic to the exact sequence associated to the adiabatic deformation of the Lie groupoid . We then generalize this result to the context of smoothly stratified manifolds. Finally, we show, by means of the aforementioned isomorphism, that the -classes associated to a metric with a positive scalar curvature defined by Piazza and Schick (2014) correspond to the -classes defined by Zenobi (2019).
Cite this article
Vito Felice Zenobi, The adiabatic groupoid and the Higson–Roe exact sequence. J. Noncommut. Geom. 15 (2021), no. 3, pp. 797–827
DOI 10.4171/JNCG/422