Leva Beklaryan. The classification theorem for groups of homeomorphisms of the line. Nonamenability of Thompson's group F
Natural Sciences / Mathematics / Combinatorics
Submitted on: Jul 02, 2012, 19:41:27
Description: 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.