A finitely generated group has two essentially free probability-measure-preserving actions with different costs: its Bernoulli action has cost strictly greater than one, while a suitable finite-height extension has cost closer to one.
A finitely generated group has two essentially free probability-measure-preserving actions with different costs: its Bernoulli action has cost strictly greater than one, while a suitable finite-height extension has cost closer to one.
A finitely generated group has two essentially free probability-measure-preserving actions with different costs: its Bernoulli action has cost strictly greater than one, while a suitable finite-height extension has cost closer to one.
If correct, gives a negative answer to Gaboriau’s general fixed-price problem.
Can one group have essentially free actions with different costs?
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