Geodesic
Amenable groups that act on the line
Morris, Dave Witte1
1Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, Alberta, T1K 3M4, Canada
Algebraic and Geometric Topology, Tome 6 (2006) no. 5, pp. 2509-2518
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Let Γ be a finitely generated, amenable group. Using an idea of É Ghys, we prove that if Γ has a nontrivial, orientation-preserving action on the real line, then Γ has an infinite, cyclic quotient. (The converse is obvious.) This implies that if Γ has a faithful action on the circle, then some finite-index subgroup of Γ has the property that all of its nontrivial, finitely generated subgroups have infinite, cyclic quotients. It also means that every left-orderable, amenable group is locally indicable. This answers a question of P Linnell.

DOI : 10.2140/agt.2006.6.2509
Keywords: amenable, action on the line, action on the circle, ordered group, indicable, cyclic quotient

Morris, Dave Witte  1

1 Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, Alberta, T1K 3M4, Canada 
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Morris, Dave Witte. Amenable groups that act on the line. Algebraic and Geometric Topology, Tome 6 (2006) no. 5, pp. 2509-2518. doi: 10.2140/agt.2006.6.2509

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