2023/04/09 by Victor Guba, Guba, Victor
Mathematics · Computer Science · #Geometric and Algebraic Topology #Advanced Operator Algebra Research #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2304.04322
A (discrete) group is called amenable whenever there exists a finitely additive right invariant probablity measure on it. For Thompson's group F the problem whether it is amenable is a long-standing open question. We consider presentation of F in terms of non-spherical semigroup diagrams. There is a natural partition of F into 7 parts in terms of these diagrams. We show that for any measure with the above properties on F, all but one of these sets have zero measure. This helps to clarify the structure of Folner sets in F provided the group is amenable.