Some applications of commutators

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Date(s) - 07/11/2017
11 h 00 min - 12 h 00 min


To a group action and a sigma-algebra of clopen sets on some space, we associate a `controlled group action’, where the action of the group can depend on events in the sigma-algebra. We discuss the basic properties of this definition, and then give some applications when the controlled group is perfect, arising from a simple commutator trick. Applications are given in two contexts related to logical gates, and in two contexts related to groups of symbolic-dynamical origin. We also get a short proof of the classical fact that there are uncountably many non-isomorphic finitely generated groups.

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