Land, Markus and Nikolaus, Thomas (2018) On the relation between K- and L-theory of C*-algebras. MATHEMATISCHE ANNALEN, 371 (1-2). pp. 517-563. ISSN 0025-5831, 1432-1807
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We prove the existence of a map of spectra between connective topological K-theory and connective algebraic L-theory of a complex -algebra A which is natural in A and compatible with multiplicative structures. We determine its effect on homotopy groups and as a consequence obtain a natural equivalence of periodic K- and L-theory spectra after inverting 2. We show that this equivalence extends to K- and L-theory of real -algebras. Using this we give a comparison between the real Baum-Connes conjecture and the L-theoretic Farrell-Jones conjecture. We conclude that these conjectures are equivalent after inverting 2 if and only if a certain completion conjecture in L-theory is true.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CATEGORIES; HOMOLOGY; LOCALIZATION; SPECTRA; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 11 Mar 2020 12:16 |
| Last Modified: | 11 Mar 2020 12:16 |
| URI: | https://pred.uni-regensburg.de/id/eprint/14545 |
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