On conjectures of Mathai and Borel (Q1771150)

It was conjectured by Mathai that the Cheeger-Gromov invariant \(\rho_{(2)} = \eta_{(2)}-\eta\) is a homotopy invariant of closed manifolds with torsion free fundamental group. This paper proves the conjecture assuming the rational Borel conjecture that the assembly map \(\alpha: \, H_*(B\Gamma,Q) \rightarrow L_*(\Gamma) \otimes Q\) is an isomorphism where \(\Gamma\) is the fundamental group.