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.
"Free group automorphisms, invariant orderings and topological applications." Algebr. Geom. Topol. 1 (1) 311 - 319, 2001. https://doi.org/10.2140/agt.2001.1.311