Journal article
OE and W∗ superrigidity results for actions by surface braid groups
Proceedings of the London Mathematical Society, Vol.111(6), pp.1431-1470
2015
DOI: 10.1112/plms/pdv058
Abstract
We show that several important normal subgroups Γ of the mapping class group of a surface satisfy the following property: any free, ergodic, probability measure‐preserving action Γ ↷ X is stably O E ‐superrigid. These include the central quotients of most surface braid groups and most Torelli groups and Johnson kernels. In addition, we show that all these groups satisfy the measure equivalence rigidity and we describe all their lattice‐embeddings. Using these results in combination with previous results from Chifan–Ioana–Kida [‘ W * ‐superrigidity for arbitrary actions of central quotients of braid groups’, Math. Ann . 361 (2015) 925–959], we deduce that any free, ergodic, probability measure‐preserving action of almost any surface braid group is stably W * ‐superrigid, that is, it can be completely reconstructed from its von Neumann algebra.
Details
- Title: Subtitle
- OE and W∗ superrigidity results for actions by surface braid groups
- Creators
- Ionut ChifanYoshikata Kida
- Resource Type
- Journal article
- Publication Details
- Proceedings of the London Mathematical Society, Vol.111(6), pp.1431-1470
- DOI
- 10.1112/plms/pdv058
- ISSN
- 0024-6115
- eISSN
- 1460-244X
- Language
- English
- Date published
- 2015
- Academic Unit
- Mathematics
- Record Identifier
- 9983985803502771
Metrics
12 Record Views