Journal article
𝑊∗-Superrigidity for arbitrary actions of central quotients of braid groups
Mathematische annalen, Vol.361(3-4), pp.563-582
04/01/2015
DOI: 10.1007/s00208-014-1077-8
Abstract
For any let be the quotient of the braid group through its center. We prove that any free ergodic probability measure preserving (pmp) action is virtually -superrigid in the following sense: if , for an arbitrary free ergodic pmp action , then the actions are virtually conjugate. Moreover, we prove that the same holds if is replaced with a finite index subgroup of the direct product , for some . The proof uses the dichotomy theorem for normalizers inside crossed products by free groups from Popa and Vaes (212, 141-198, 2014) in combination with the OE superrigidity theorem for actions of mapping class groups from Kida (131, 99-109, 2008). Similar techniques allow us to prove that if a group is hyperbolic relative to a finite family of proper, finitely generated, residually finite, infinite subgroups, then the factor has a unique Cartan subalgebra, up to unitary conjugacy, for any free ergodic pmp action . Gamma (X, mu).
Details
- Title: Subtitle
- 𝑊∗-Superrigidity for arbitrary actions of central quotients of braid groups
- Creators
- Ionut Chifan - University of IowaAdrian Ioana - University of California San DiegoYoshikata Kida - Kyoto University
- Resource Type
- Journal article
- Publication Details
- Mathematische annalen, Vol.361(3-4), pp.563-582
- DOI
- 10.1007/s00208-014-1077-8
- ISSN
- 0025-5831
- eISSN
- 1432-1807
- Publisher
- SPRINGER HEIDELBERG
- Number of pages
- 20
- Grant note
- 1161047 / NSF Grant DMS 1301370 / NSF 1253402 / NSF Career Grant DMS
- Language
- English
- Date published
- 04/01/2015
- Academic Unit
- Mathematics
- Record Identifier
- 9984242454002771
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