Geodesic
Non-Left-Orderable 3-Manifold Groups
Canadian mathematical bulletin, Tome 48 (2005) no. 1, pp. 32-40

Voir la notice de l'article provenant de la source Cambridge University Press

We show that several torsion free 3-manifold groups are not left-orderable. Our examples are groups of cyclic branched coverings of ${{S}^{3}}$ branched along links. The figure eight knot provides simple nontrivial examples. The groups arising in these examples are known as Fibonacci groups which we show not to be left-orderable. Many other examples of non-orderable groups are obtained by taking 3-fold branched covers of ${{S}^{3}}$ branched along various hyperbolic 2-bridge knots. The manifold obtained in such a way from the ${{5}_{2}}$ knot is of special interest as it is conjectured to be the hyperbolic 3-manifold with the smallest volume.
DOI : 10.4153/CMB-2005-003-6
Mots-clés : 57M25, 57M12, 20F60 
Dąbkowski, Mieczysław K.; Przytycki, Józef H.; Togha, Amir A. Non-Left-Orderable 3-Manifold Groups. Canadian mathematical bulletin, Tome 48 (2005) no. 1, pp. 32-40. doi: 10.4153/CMB-2005-003-6
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