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Amenable groups that act on the line

Dave Witte Morris
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Abstract

Let Gamma be a finitely generated, amenable group. Using an idea of E Ghys, we prove that if Gamma has a nontrivial, orientation-preserving action on the real line, then Gamma has an infinite, cyclic quotient. (The converse is obvious.) This implies that if Gamma has a faithful action on the circle, then some finite-index subgroup of Gamma 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.

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BibTeXRIS

Dave Witte Morris. 2009-07-29. Amenable groups that act on the line. https://doi.org/10.2140/agt.2006.6.2509

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