Entropy theory for sofic groupoids I: The foundations |
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Authors: | Lewis Bowen |
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Affiliation: | 1. Department of Mathematics, University of Texas, Austin, TX, 78712, USA
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Abstract: | This is the first part in a series in which sofic entropy theory is generalized to class-bijective extensions of sofic groupoids. Here we define topological and measure entropy and prove invariance. We also establish the variational principle, compute the entropy of Bernoulli shift actions and answer a question of Benjy Weiss pertaining to the isomorphism problem for non-free Bernoulli shifts. The proofs are independent of previous literature. |
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