A note on semi-conjugacy for circle actions
Geometric Topology
2016-06-08 v3 Differential Geometry
Group Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1410.8350,
title = {A note on semi-conjugacy for circle actions},
author = {Michelle Bucher and Roberto Frigerio and Tobias Hartnick},
journal= {arXiv preprint arXiv:1410.8350},
year = {2016}
}
Comments
39 pages. Improved version of the previous manuscript, incorporating further historical remarks and a discussion of the equivalence between semiconjugacy and monotone equivalence