Amenability of Thompson’s group F

Determine whether Thompson’s group F is amenable. Establish either amenability or non-amenability of Thompson’s group F to clarify its status and implications for complexity results that hinge on amenability properties.

Background

In discussing average-case complexity in amenable groups, the paper highlights several examples where linear average-case complexity holds, including Thompson’s group F. The authors note that many techniques for average-case analysis rely on amenability properties, making the amenability status of F highly consequential.

Amenability affects cogrowth rates and the applicability of the parallel algorithm strategy used for non-amenable groups. Resolving whether F is amenable would have implications for methods in average-case complexity and for broader questions in geometric and combinatorial group theory.