Higher rho-invariants and the surgery structure set

Details Higher rho-invariants and the surgery structure set Higher rho-invariants and the surgery structure set

2010-08-21

arxiv.org/abs/1008.3644v3

Mathematics

Differential Geometry

40 pages; some technicalities corrected, compatibility with L-theory group action added

Scientific paper

We study noncommutative eta- and rho-forms for homotopy equivalences. We prove a product formula for them and show that the rho-forms are well-defined on the structure set. We also define an index theoretic map from L-theory to C*-algebraic K-theory and show that it is compatible with the rho-forms. Our approach, which is based on methods of Hilsum-Skandalis and Piazza-Schick, also yields a unified analytic proof of the homotopy invariance of the higher signature class and of the L^2-signature for manifolds with boundary.

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