A note on semi-conjugacy for circle actions
  We define a notion of semi-conjugacy between orientation-preserving actions of a group on the circle, which for fixed point free actions coincides with a classical definition of Ghys. We then show that two circle actions are semi-conjugate if and only if they have the same bounded Euler class. This settles some existing confusion present in the literature. 
Michelle Bucher, Roberto Frigerio, Tobias Hartnick
math.GT math.DG math.GR