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

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

2011-12-08

arxiv.org/abs/1112.1942v2

Mathematics

Group Theory

17 pages, 3 figures; corrected typos in Theorem B

Scientific paper

This paper allows one to obtain a criterion for the existence of a projective-invariant measure formulated in terms of combinatorial properties of a group (amenability of some canonical quotient group). This criterion is the most important classification instrument and it is a basis of the classification scheme for groups of homeomorphisms of the line. In particular, a nonamenability of Thompson's group $F$ follows from the obtained criterion for the existence of a projective-invariant measure.

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