Non-left-orderable 3-manifold groups
Geometric Topology
2016-09-07 v2 Group Theory
Abstract
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.
Keywords
Cite
@article{arxiv.math/0302098,
title = {Non-left-orderable 3-manifold groups},
author = {Mieczyslaw K. Dabkowski and Jozef H. Przytycki and Amir A. Togha},
journal= {arXiv preprint arXiv:math/0302098},
year = {2016}
}
Comments
To appear in Canadian Mathematical Bull.; 12 pages, 5 figures