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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 $widetilde{X}times_Gammawidetilde{X}$. 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.
The main result of this paper is a new and direct proof of the natural transformation from the surgery exact sequence in topology to the analytic K-theory sequence of Higson and Roe. Our approach makes crucial use of analytic properties and new ind
In this article we extend the Bloch-Wigner exact sequence over local rings, where their residue fields have more than nine elements. Moreover, we prove Van der Kallens theorem on the presentation of the second $K$-group of local rings such that their
In this paper, we define the relative higher $rho$ invariant for orientation preserving homotopy equivalence between PL manifolds with boundary in $K$-theory of the relative obstruction algebra, i.e. the relative analytic structure group. We also sho
We introduce the notion of proper Kasparov cycles for Kasparovs G-equivariant KK-theory for a general locally compact, second countable topological group G. We show that for any proper Kasparov cycle, its induced map on K-theory factors through the l
Let $X$ be a compact Hausdorff space, let $Gamma$ be a discrete group that acts continuously on $X$ from the right, define $widetilde{X} = {(x,gamma) in X times Gamma : xcdotgamma= x}$, and let $Gamma$ act on $widetilde{X}$ via the formula $(x,gamma)