Free group automorphisms, invariant orderings and topological applications

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

References

Forward citations

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

Volume 1, issue 1 (2001)

Dale Rolfsen and Bert Wiest