L^2 rho form for normal coverings of fibre bundles

Details L^2 rho form for normal coverings of fibre bundles L^2 rho form for normal coverings of fibre bundles

2007-04-06

arxiv.org/abs/0704.0909v2

Int. J. Math. 22 (2011), no. 8, pp. 1139-1161

Mathematics

Geometric Topology

21 pages, revised version

Scientific paper

10.1142/S0129167X11007161

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.

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