Algebraic and Geometric Topology 1 (2001), paper no. 15, pages 311-319.

Free group automorphisms, invariant orderings and topological applications

Dale Rolfsen, Bert Wiest

Abstract. We are concerned with orderable groups and particularly those with orderings invariant not only under multiplication, but also under a given automorphism or family of automorphisms. Several applications to topology are given: we prove that the fundamental groups of hyperbolic nonorientable surfaces, and the groups of certain fibred knots are bi-orderable. Moreover, we show that the pure braid groups associated with hyperbolic nonorientable surfaces are left-orderable.

Keywords. Ordered group, surface group, knot group, surface braid group

AMS subject classification. Primary: 6F15. Secondary: 57M05.

DOI: 10.2140/agt.2001.1.311

E-print: arXiv:math.GR/0105205

Submitted: 8 February 2001. (Revised: 16 May 2001.) Accepted: 22 May 2001. Published: 24 May 2001.

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Dale Rolfsen, Bert Wiest
Mathematics Department, University of British Columbia
1984 Mathematics Road, Vancouver BC, Canada V6T 1Z2

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