The 4-string Braid group $B_4$ has property RD and exponential mesoscopic rank
| dc.creator | Barré, Sylvain | |
| dc.creator | Pichot, Mikael | |
| dc.date | 2008-09-03 | |
| dc.date | 2009-02-03 | |
| dc.date.accessioned | 2026-07-07T12:36:43Z | |
| dc.date.available | 2026-07-07T12:36:43Z | |
| dc.description | We prove that the braid group $B_4$ on 4 strings, as well as its central quotient $B_4/< z>$, have the property RD of Haagerup-Jolissaint. It follows that the automorphism group $\Aut(F_2)$ of the free group $F_2$ on 2 generators has property RD. We also prove that the braid group $B_4$ is a group of intermediate rank (of dimension 3). Namely, we show that both $B_4$ and its central quotient have exponential mesoscopic rank, i.e., that they contain exponentially many large flat balls which are not included in flats. | |
| dc.description | reference added, minor corrections | |
| dc.identifier | https://arxiv.org/abs/0809.0645 | |
| dc.identifier | http://arxiv.org/abs/0809.0645 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/218193 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | Operator Algebras | |
| dc.title | The 4-string Braid group $B_4$ has property RD and exponential mesoscopic rank | |
| dc.type | text |