Non-left-orderable 3-manifold groups

Details Non-left-orderable 3-manifold groups Non-left-orderable 3-manifold groups

2003-02-10

arxiv.org/abs/math/0302098v2

Mathematics

Geometric Topology

To appear in Canadian Mathematical Bull.; 12 pages, 5 figures

Scientific paper

We show that several torsion free 3-manifold groups are not left-orderable. Our examples are groups of cyclic branched covers 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.

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