Preprint in the OpenAI Math release
A group without fixed price
OpenAI
Abstract
We construct a finitely generated group with two essentially free probability-measure-preserving actions of different costs. This gives a negative answer to Gaboriau's general fixed-price problem. The group is an amalgam of a free group of rank 100 with a direct product. Its Bernoulli action has cost bounded away from one, whereas finite height extensions have costs tending to one.
open until 1 Jan 2028
est. 50% chance this result is independently verified by the end of 2027.
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