An extension criterion for lattice actions on the circle
Group Theory
2009-05-04 v1
Abstract
We establish a necessary and sufficient condition for an action of a lattice by homeomorphisms of the circle to extend continuously to the ambient locally compact group. This condition is expressed in terms of the real bounded Euler class of this action. Combined with classical vanishing theorems in bounded cohomology, one recovers rigidity results of Ghys, Witte--Zimmer, Navas and Bader--Furman--Shaker in a unified manner.
Cite
@article{arxiv.0905.0136,
title = {An extension criterion for lattice actions on the circle},
author = {Marc Burger},
journal= {arXiv preprint arXiv:0905.0136},
year = {2009}
}