Sofic mean dimension
Abstract
We introduce mean dimensions for continuous actions of countable sofic groups on compact metrizable spaces. These generalize the Gromov-Lindenstrauss-Weiss mean dimensions for actions of countable amenable groups, and are useful for distinguishing continuous actions of countable sofic groups with infinite entropy.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2011
- DOI:
- 10.48550/arXiv.1105.0140
- arXiv:
- arXiv:1105.0140
- Bibcode:
- 2011arXiv1105.0140L
- Keywords:
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- Mathematics - Dynamical Systems
- E-Print:
- 40 pages. To appear in Adv. Math