## Amenable groups that are left orderable

- Date: 03/20/2007

Lecturer(s):

Dave Morris (University of Lethbridge)

Location:

University of British Columbia

Topic:

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