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Geometriae Dedicata

, Volume 136, Issue 1, pp 1–15 | Cite as

Properties of Richard Thompson’s group F related to Følner sets

  • John DonnellyEmail author
Original Paper

Abstract

The group F was invented in the 1960s by Richard Thompson, and is a subgroup of the group of all piecewise linear, orientation preserving homeomorphisms of the unit interval. R. Geoghegan has conjectured that F is an example of a finitely presented nonamenable group which has no free subgroup on two generators. In this article, we study properties of F related to amenability. We state some necessary conditions that a sequence of nonempty finite subsets of F must satisfy to be a sequence of Følner sets of F.

Keywords

Richard Thompson’s group F Følner sets Ruinous sets Thin sets Amenability 

Mathematics Subject Classification (2000)

20M99 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of MathematicsMount Union CollegeAllianceUSA

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