The classification theorem for groups of homeomorphisms of the line.\n Nonamenability of Thompson's group F

2011/12/08 by L. A. Beklaryan, Beklaryan, Leva
Computer Science · Mathematics · #20Exx #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1112.1942

openalex publication_date 2011/12/08 · openalex created_date 2022/08/31 · openalex updated_date 2026/07/28

Abstract

This paper allows one to obtain a criterion for the existence of a\nprojectively invariant measure formulated in terms of combinatorial properties\nof a group (amenability of some canonical quotient group). Such necessary and\nsufficient condition is a basis of the classification scheme for groups of\nhomeomorphisms of the line. In particular, a nonamenability of Thompson's group\nF follows from the obtained criterion.\n

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