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Organizers |
Non-left-orderable 3-manifold groups
by
Amir A. Togha
George Washington University
Coauthors: Mieczyslaw K. Dabkowski (UTD), Jozef H. Przytycki (GWU)
We show that several torsion free 3-manifold groups are not left-orderable. Our examples are groups of cyclic branched covers of S3 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 S3 branched along various hyperbolic 2-bridge knots. The manifold obtained in such a way from the 52 knot is of special interest as it is conjectured to be the hyperbolic 3-manifold with the smallest volume.
Date received: December 3, 2003
Copyright © 2003 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # camw-09.