Amenable groups that are left orderable

  • Date: 03/20/2007

Dave Morris (University of Lethbridge)


University of British Columbia


Let G be an abstract group. It is known that if every finitely
generated subgroup of G has an infinite cyclic quotient, then G is left
orderable. Using an idea of E.Ghys, we prove that the converse is true
for all amenable groups. (This generalizes the known fact that the
converse is true for all solvable groups.) The proof is surprisingly
easy, and combines amenability with group theory, elementary topology,
and the Poincare Recurrence Theorem (a basic result in the theory of
dynamical systems).

Other Information: 

Algebraic Topology Seminar 2007