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arXiv · 1112.1942

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

Leva Beklaryan
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Abstract

This paper allows one to obtain a criterion for the existence of a projectively invariant measure formulated in terms of combinatorial properties of a group (amenability of some canonical quotient group). Such necessary and sufficient condition 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.

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Leva Beklaryan. 2012-11-25. The classification theorem for groups of homeomorphisms of the line. Nonamenability of Thompson's group $F$. https://arxiv.org/abs/1112.1942

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