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Orderable 3-manifold groups

Steven Boyer, Dale Rolfsen, Bert Wiest (2005)

Annales de l’institut Fourier

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...

Principal congruence link complements

Mark D. Baker, Alan W. Reid (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper we study principal congruence link complements in S 3 . It is known that there are only finitely many such link complements, and we make a start on enumerating them using a combination of theoretical methods and computer calculations with MAGMA.

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