Orderable 3-manifold groups
by
Steven Boyer
Université du Québec à Montréal
Coauthors: Dale Rolfsen (University of British Columbia), Bert Wiest (Université de Rennes I)

We investigate the orderability properties of fundamental groups of 3-dimensional manifolds. Many 3-manifold groups support left-invariant orderings, including all compact ¶²-irreducible manifolds with positive first Betti number. For seven of the eight geometries (excluding hyperbolic) we are able to characterize which manifolds' groups support a left-invariant or bi-invariant ordering. We also show that manifolds modelled on these geometries have virtually bi-orderable groups. The question of virtual orderability of 3-manifold groups in general, and even hyperbolic manifolds, remains open, and is closely related to conjectures of Waldhausen and others.

Date received: February 22, 2002