Volume 1, issue 1 (2001)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Free group automorphisms, invariant orderings and topological applications

Dale Rolfsen and Bert Wiest

Algebraic & Geometric Topology 1 (2001) 311–319

arXiv: math.GR/0105205

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
Mathematical Subject Classification 2000
Primary: 6F15
Secondary: 57M05
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Publication
Received: 8 February 2001
Revised: 16 May 2001
Accepted: 22 May 2001
Published: 24 May 2001
Authors
Dale Rolfsen
Mathematics Department
University of British Columbia
1984 Mathematics Road
Vancouver BC
Canada V6T 1Z2
Bert Wiest
Mathematics Department
University of British Columbia
1984 Mathematics Road
Vancouver BC
Canada V6T 1Z2