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Article Dans Une Revue Journal of Functional Analysis Année : 2015

The Higson-Roe exact sequence and $\ell^2$ eta invariants

Résumé

The goal of this paper is to solve the problem of existence of an $\ell^2$ relative eta morphism on the Higson-Roe structure group. Using the Cheeger-Gromov $\ell^2$ eta invariant, we construct a group morphism from the Higson-Roe maximal structure group constructed in [HiRo:10] to the reals. 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 $\ell^2$ rho invariant. When we apply this morphism to the structure class associated with an oriented homotopy equivalence, we get the difference of the $\ell^2$ rho invariants of the corresponding signature operators. We thus get new proofs for the classical $\ell^2$ rigidity theorems of Keswani obtained in [Ke:00].

Dates et versions

hal-01819165 , version 1 (20-06-2018)

Identifiants

Citer

Moulay Tahar Benameur, Indrava Roy. The Higson-Roe exact sequence and $\ell^2$ eta invariants. Journal of Functional Analysis, 2015, 268 (4), pp.974-1031. ⟨10.1016/j.jfa.2014.11.006⟩. ⟨hal-01819165⟩
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