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The twisted coarse Baum-Connes conjecture with coefficients in coarsely proper algebras.
- Source :
-
Journal of Functional Analysis . Oct2023, Vol. 285 Issue 8, pN.PAG-N.PAG. 1p. - Publication Year :
- 2023
-
Abstract
- We introduce a notion of (approximately) coarsely proper algebras for coarse embeddings of metric spaces to formulate and prove a version of twisted coarse Baum-Connes conjecture with coefficients in coarsely proper algebras. This may be regarded as a coarse geometric version of the generalized Green-Julg Theorem in the Baum-Connes conjecture for countable discrete groups. It also provides a conceptual framework for the Dirac-dual-Dirac method to the coarse Novikov conjecture for coarse embeddings into several different spaces, including Hilbert spaces, simply connected complete Riemannian manifolds with non-positive sectional curvature, Banach spaces with property (H) and Hilbert-Hadamard spaces. Moreover, for a group extension 1 → N → G → Q → 1 , we show that if N is coarsely embeddable into Hilbert space and Q is coarsely embeddable into an admissible Hilbert-Hadamard space, then the coarse Novikov conjecture holds for G. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00221236
- Volume :
- 285
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Journal of Functional Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 167369287
- Full Text :
- https://doi.org/10.1016/j.jfa.2023.110067