Engel, Alexander and Marcinkowski, Michal (2020) Burghelea conjecture and asymptotic dimension of groups. JOURNAL OF TOPOLOGY AND ANALYSIS, 12 (2). pp. 321-356. ISSN 1793-5253, 1793-7167
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We review the Burghelea conjecture, which constitutes a full computation of the periodic cyclic homology of complex group rings, and its relation to the algebraic Baum-Connes conjecture. The Burghelea conjecture implies the Bass conjecture. We state two conjectures about groups of finite asymptotic dimension, which together imply the Burghelea conjecture for such groups. We prove both conjectures for many classes of groups. It is known that the Burghelea conjecture does not hold for all groups, although no finitely presentable counterexample was known. We construct a finitely presentable (even type F-infinity) counterexample based on Thompson's group F. We construct as well a finitely generated counterexample with finite decomposition complexity.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | RELATIVELY HYPERBOLIC GROUPS; COHOMOLOGICAL DIMENSION; NOVIKOV-CONJECTURE; CYCLIC HOMOLOGY; GROUP-ALGEBRA; K-THEORY; FINITE; DECOMPOSITION; CENTRALIZERS; IDEALS; Burghelea conjecture; asymptotic dimension; cohomological dimension; centralizers |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 22 Mar 2021 12:06 |
| Last Modified: | 22 Mar 2021 12:06 |
| URI: | https://pred.uni-regensburg.de/id/eprint/44453 |
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