Invariant group orderings and Galois conjugates
  This paper investigates conditions under which a given automorphism of a residually torsion-free nilpotent group respects some ordering of the group. For free groups and surface groups, this has relevance to ordering the fundamental groups of three-dimensional manifolds which fibre over the circle. 
Peter A. Linnell, Akbar H. Rhemtulla and Dale P. O. Rolfsen