Amenability problem for Thompson's group $F$: state of the art

Abstract

This is a survey of our recent results on the amenability problem for Thompson's group $F$. They mostly concern esimating the density of finite subgraphs in Cayley graphs of $F$ for various systems of generators, and also equations in the group ring of $F$. We also discuss possible approaches to solve the problem in both directions.

24 pages, 2 figures. Published in journal of Groups, Complexity, Cryptology. arXiv admin note: text overlap with arXiv:2112.09812

References in corpus (4)

• Amenability and paradoxical decompositions for pseudogroups and for discrete metric spaces
• Systems of equations over the group ring of Thompson's group $F$
• Cayley graphs of R. Thompson's group F: new estimates for the density
• On zero-measured subsets of Thompson's group F