1. CMB 2010 (vol 53 pp. 706)
|Non-Right-Orderable 3-Manifold Groups|
We exhibit infinitely many hyperbolic $3$-manifold groups that are not right-orderable.
Categories:20F60, 57M05, 57M50
2. CMB 2005 (vol 48 pp. 32)
|Non-Left-Orderable 3-Manifold Groups |
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. %with various hyperbolic 2-bridge knots as branched sets. 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.
Categories:57M25, 57M12, 20F60