Higher rho-invariants and the surgery structure set
Differential Geometry
2014-02-26 v4 K-Theory and Homology
Abstract
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.
Cite
@article{arxiv.1008.3644,
title = {Higher rho-invariants and the surgery structure set},
author = {Charlotte Wahl},
journal= {arXiv preprint arXiv:1008.3644},
year = {2014}
}
Comments
42 pages; exposition improved; version accepted by Journal of Topology