The Higson-Roe exact sequence and l(2) eta invariants

摘要

The goal of this paper is to solve the problem of existence of an l(2) relative eta morphism on the Higson-Roe structure group. Using the Cheeger-Gromov l(2) eta invariant, we construct a group morphism from the Higson-Roe maximal structure group constructed in [35] to the reels. When we apply this morphism to the structure class associated with the spin Dirac operator for a metric of positive scalar curvature, we get the spin l(2) rho invariant. When we apply this morphism to the structure class associated with an oriented homotopy equivalence, we get the difference of the V rho invariants of the corresponding signature operators. We thus get new proofs for the classical l(2) rigidity theorems of Keswani obtained in [41]. (C) 2014 Elsevier Inc. All rights reserved.