Orderable 3-manifold groups

Boyer, Steven; Rolfsen, Dale; Wiest, Bert

Orderable 3-manifold groups

Authors

Boyer, Steven

Rolfsen, Dale

Wiest, Bert

Description

We investigate the orderability properties of fundamental groups of 3-dimensional manifolds. Many 3-manifold groups support left-invariant orderings, including all compact P^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.
37 pages. Published version. Improvements in the organisation and presentation of the material