Bunke, Ulrich (2018) A regulator for smooth manifolds and an index theorem. JOURNAL OF NONCOMMUTATIVE GEOMETRY, 12 (4). pp. 1293-1340. ISSN 1661-6952, 1661-6960
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For a smooth manifold X and an integer d > dim(X) we construct and investigate a natural map sigma(d) : K-d (C-infinity (X)) -> ku C/Z(-d-1)(X). Here K-d (C-infinity(X)) is the algebraic K-theory group of the algebra of complex valued smooth functions on X, and ku C/Z* is the generalized cohomology theory called connective complex K-theory with coefficients in C/Z. If the manifold X is closed of odd dimension d - 1 and equipped with a Dirac operator (sic), then we state and partially prove the conjecture stating that the following two maps K-d (C-infinity(X)) -> C/Z coincide: 1. Pair the result of sigma(d) with the K-homology class of (sic). 2. Compose the Connes-Karoubi multiplicative character with the classifying map of the d-summable Fredholm module of (sic).
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ALGEBRAIC K-THEORY; SPECTRAL ASYMMETRY; HOMOLOGY; Regulators; differential cohomology; algebraic K-theory of smooth functions; Connes-Karoubi character |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Ulrich Bunke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 20 Mar 2020 06:26 |
| Last Modified: | 20 Mar 2020 06:26 |
| URI: | https://pred.uni-regensburg.de/id/eprint/15244 |
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