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. is claries some existing confusion present in the literature.
Cite this article
Michelle Bucher, Roberto Frigerio, Tobias Hartnick, A note on semi-conjugacy for circle actions. Enseign. Math. 62 (2016), no. 3/4, pp. 317–360DOI 10.4171/LEM/62-3/4-1