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KNOTS in WASHINGTON XV (2nd Japan-USA Workshop in Knot Theory)
January 10-15, 2003
George Washington University and Johns Hopkins University
Washington, DC and Baltimore, MD, USA

Organizers
Kazuaki Kobayashi, Jozef H. Przytycki, Yongwu Rong, Shin-ichi Suzuki, Kouki Taniyama, Tatsuya Tsukamoto, Akira Yasuhara

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Non-left-orderable 3-manifold groups I
by
Ataollah Togha
The George Washington University
Coauthors: Mieczyslaw K. Dabkowski, Jozef H. Przytycki

We show that several torsion free 3-manifold groups are not left-orderable. Our examples arise from considering cyclic branched covers of S3 with links as branched sets. 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-left-orderable groups are obtained by taking 3-fold branched covers with various hyperbolic 2-bridge knots as branched sets. The manifold obtained in such a way from the 52 knot is of special interest since it is conjectured to be the hyperbolic 3-manifold with the smallest volume.

Date received: January 7, 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 # cajr-29.