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Free group automorphisms, invariant orderings and topological applications

Dale Rolfsen·Bert Wiest
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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.

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Dale Rolfsen, Bert Wiest. 2001-05-25. Free group automorphisms, invariant orderings and topological applications. https://doi.org/10.2140/agt.2001.1.311

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