Free group automorphisms, invariant orderings and topological applications

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.

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

References in corpus (2)

• Orderings of mapping class groups after Thurston
• Ordering pure braid groups on closed surfaces

Cited by in corpus (9)

• Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups
• Limit groups as limits of free groups: compactifying the set of free groups
• A survey of surface braid groups and the lower algebraic K-theory of their group rings
• Borel structures on the space of left-orderings
• Braids, orderings and minimal volume cusped hyperbolic 3-manifolds
• A note on geometric constructions of bi-invariant orderings
• Low Dimensional Topology and Ordering Groups
• Invariant group orderings and Galois conjugates
• Compactness of the space of left orders