1. CMB 2010 (vol 53 pp. 706)
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
%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