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EnglishLet M be a closed manifold and α: π 1 (M) → Un a representation. We give a purely K-theoretic description of the associated element in the K-theory group of M with ℝ/ℤ-coefficients ([α] ∈ K 1 (M;ℝ/ℤ)). To that end, it is convenient to describe the ℝ/ℤ-K-theory as a relative K-theory of the unital inclusion of ℂ into a finite von Neumann algebra B. We use the following fact: there is, associated with α, a finite von Neumann algebra B together with a flat bundle ε → M with fibers B, such that Eα ⊗ ε is canonically isomorphic with ℂn ⊗ ε, where Eα denotes the flat bundle with fiber ℂn associated with α. We also discuss the spectral flow and rho type description of the pairing of the class [α] with the K-homology class of an elliptic selfadjoint (pseudo)-differential operator D of order 1. Copyright © ISOPP 2014.
| Titolo: | Flat bundles, von Neumann algebras and K-theory with R/Z-coefficients | |
| Autori: | Antonini P.; Azzali S.; Skandalis G. | |
| Rivista: | ||
| Data di pubblicazione: | 2014 | |
| Volume: | 13 | |
| Fascicolo: | 2 | |
| Pagina iniziale: | 275 | |
| Pagina finale: | 303 | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1017/is014001024jkt253 | |
| URL: | https://arxiv.org/abs/1308.0218 | |
| Appare nelle tipologie: | 1.1 Journal article |
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http://hdl.handle.net/20.500.11767/32467
