Orderable 3-manifold groups

Steven Boyer; Dale Rolfsen; Bert Wiest

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Orderable 3-manifold groups

Steven Boyer·Dale Rolfsen·Bert Wiest

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Abstract

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.

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BibTeX RIS

Steven Boyer, Dale Rolfsen, Bert Wiest. 2005-06-14. Orderable 3-manifold groups. https://arxiv.org/abs/math/0211110

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