Algebraic & Geometric Topology 1 (2001) 311–319

DOI: 10.2140/agt.2001.1.311

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

Primary: 6F15

Secondary: 57M05

References

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Publication

Received: 8 February 2001
Revised: 16 May 2001
Accepted: 22 May 2001
Published: 24 May 2001

Authors