Free group automorphisms, invariant orderings and topological applications

Details Free group automorphisms, invariant orderings and topological applications Free group automorphisms, invariant orderings and topological applications

2001-05-25

arxiv.org/abs/math/0105205v1

Algebr. Geom. Topol. 1 (2001) 311-319

Mathematics

Group Theory

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-15.abs.html

Scientific paper

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.

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