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On orderability of fibred knot groups

Published online by Cambridge University Press:  26 June 2003

BERNARD PERRON  and
DALE ROLFSEN
BERNARD PERRON
Affiliation:
Laboratoire de Topologie, Université de Bourgogne, BP 47870 21078 - Dijon Cedex, France. e-mail: [email protected]
DALE ROLFSEN
Affiliation:
Pacific Institute for the Mathematical Sciences and Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z2. e-mail: [email protected]
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Abstract

It is known that knot groups are right-orderable, and that many of them are not bi-orderable. Here we show that certain fibred knots in $S^3$ (or in a homology sphere) do have bi-orderable fundamental groups. In particular, this holds for fibred knots, such as $4_1$, for which the Alexander polynomial has all roots real and positive. This is an application of the construction of orderings of groups, which are moreover invariant with respect to a certain automorphism.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 135 , Issue 1 , July 2003 , pp. 147 - 153
Copyright
2003 Cambridge Philosophical Society

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