Article contents
Equivariant
$\mathcal {O}_{2}$-absorption theorem for exact groups
Published online by Cambridge University Press: 17 June 2021
Abstract
We show that, up to strong cocycle conjugacy, every countable exact group admits a unique equivariantly $\mathcal {O}_{2}$-absorbing, pointwise outer action on the Cuntz algebra
$\mathcal {O}_{2}$ with the quasi-central approximation property (QAP). In particular, we establish the equivariant analogue of the Kirchberg
$\mathcal {O}_{2}$-absorption theorem for these groups.
MSC classification
- Type
- Research Article
- Information
- Copyright
- © 2021 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence
References
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210723074453220-0914:S0010437X21007168:S0010437X21007168_inline675.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210723074453220-0914:S0010437X21007168:S0010437X21007168_inline676.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210723074453220-0914:S0010437X21007168:S0010437X21007168_inline678.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210723074453220-0914:S0010437X21007168:S0010437X21007168_inline679.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210723074453220-0914:S0010437X21007168:S0010437X21007168_inline680.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210723074453220-0914:S0010437X21007168:S0010437X21007168_inline681.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210723074453220-0914:S0010437X21007168:S0010437X21007168_inline682.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210723074453220-0914:S0010437X21007168:S0010437X21007168_inline683.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210723074453220-0914:S0010437X21007168:S0010437X21007168_inline684.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210723074453220-0914:S0010437X21007168:S0010437X21007168_inline685.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210723074453220-0914:S0010437X21007168:S0010437X21007168_inline686.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210723074453220-0914:S0010437X21007168:S0010437X21007168_inline687.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210723074453220-0914:S0010437X21007168:S0010437X21007168_inline688.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210723074453220-0914:S0010437X21007168:S0010437X21007168_inline689.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210723074453220-0914:S0010437X21007168:S0010437X21007168_inline690.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210723074453220-0914:S0010437X21007168:S0010437X21007168_inline691.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210723074453220-0914:S0010437X21007168:S0010437X21007168_inline693.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210723074453220-0914:S0010437X21007168:S0010437X21007168_inline694.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210723074453220-0914:S0010437X21007168:S0010437X21007168_inline695.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210723074453220-0914:S0010437X21007168:S0010437X21007168_inline696.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20210723074453220-0914:S0010437X21007168:S0010437X21007168_inline697.png?pub-status=live)
- 4
- Cited by