Fournier-Facio, Francesco and Löh, Clara and Moraschini, Marco (2024) Bounded cohomology of finitely presented groups: vanishing, non-vanishing, and computability. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 25 (2). pp. 1169-1202. ISSN 0391-173X, 2036-2145
Full text not available from this repository. (Request a copy)Abstract
We provide new computations in bounded cohomology: A group is boundedly acyclic if its bounded cohomology with trivial real coefficients is zero in all positive degrees. We show that there exists a continuum of finitely generated non-amenable boundedly acyclic groups and construct a finitely presented non-amenable boundedly acyclic group. On the other hand, we construct a continuum of finitely generated groups, whose bounded cohomology has uncountable dimension in all degrees greater than or equal to 2, and a concrete finitely presented one. Countable non-amenable groups with these two extreme properties were previously known to exist, but these constitute the first finitely generated/finitely presented examples. Finally, we show that various algorithmic problems on bounded cohomology are undecidable.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SUBGROUPS; RIGIDITY |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Clara Löh |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 30 Oct 2025 07:10 |
| Last Modified: | 30 Oct 2025 07:10 |
| URI: | https://pred.uni-regensburg.de/id/eprint/64549 |
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