Abstract
We present a uniform version of a result of M. Gromov on the surjunctivity of maps commuting with expansive group actions and discuss several applications. We prove in particular that for any group Γ and any field \({\mathbb K}\) , the space of Γ-marked groups G such that the group algebra \({\mathbb {K}[G]}\) is stably finite is compact.
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We express our gratitude to the referee for her/his suggestions and remarks.
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Communicated by E. Zelmanov.
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Ceccherini-Silberstein, T., Coornaert, M. Expansive actions on uniform spaces and surjunctive maps. Bull. Math. Sci. 1, 79–98 (2011). https://doi.org/10.1007/s13373-011-0004-5
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DOI: https://doi.org/10.1007/s13373-011-0004-5
Keywords
- Expansive action
- Uniform space
- Surjunctive map
- Cellular automaton
- Shift action
- Subshift
- Group algebra
- Stable finiteness