The Higson-Roe exact sequence and $\ell^2$ eta invariants
| Autor: | Benameur, Moulay-Tahar, Roy, Indrava |
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| Rok vydání: | 2014 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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]. Comment: 40 pages; typos fixed, references added |
| Databáze: | arXiv |
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