TY  - JOUR
A1  - Antonini, Paolo
A1  - Azzali, Sara
A1  - Skandalis, Georges
T1  - Bivariant K-theory with R/Z-coefficients and rho classes of unitary representations
JF  - Journal of functional analysis
N2  - We construct equivariant KK-theory with coefficients in and R/Z as suitable inductive limits over II1-factors. We show that the Kasparov product, together with its usual functorial properties, extends to KK-theory with real coefficients. Let Gamma be a group. We define a Gamma-algebra A to be K-theoretically free and proper (KFP) if the group trace tr of Gamma acts as the unit element in KKR Gamma (A, A). We show that free and proper Gamma-algebras (in the sense of Kasparov) have the (KFP) property. Moreover, if Gamma is torsion free and satisfies the KK Gamma-form of the Baum-Connes conjecture, then every Gamma-algebra satisfies (KFP). If alpha : Gamma -> U-n is a unitary representation and A satisfies property (KFP), we construct in a canonical way a rho class rho(A)(alpha) is an element of KKR/Z1,Gamma (A A) This construction generalizes the Atiyah-Patodi-Singer K-theory class with R/Z-coefficients associated to alpha. (C) 2015 Elsevier Inc. All rights reserved.
KW  - Operator algebras
KW  - Bivariant K-theory
KW  - Rho invariants
Y1  - 2016
U6  - https://doi.org/10.1016/j.jfa.2015.06.017
SN  - 0022-1236
SN  - 1096-0783
VL  - 270
SP  - 447
EP  - 481
PB  - Elsevier
CY  - San Diego
ER  -