L^2 rho form for normal coverings of fibre bundles

Abstract

We define the secondary invariants L^2- eta and -rho forms for families of generalized Dirac operators on normal coverings of fibre bundles. On the covering family we assume transversally smooth spectral projections, and Novikov--Shubin invariants bigger than 3(dim B+1) to treat the large time asymptotic for general operators. In the particular case of a bundle of spin manifolds, we study the L^2- rho class in relation to the space of positive scalar curvature vertical metrics.

21 pages, revised version

References in corpus (3)

• Bordism, rho-invariants and the Baum-Connes conjecture
• On Invariants of Hirzebruch and Cheeger-Gromov
• Groups with torsion, bordism and rho-invariants