We describe all the group morphisms from the group of orientation-preserving homeomorphisms of the circle to the group of homeomorphisms of the annulus or of the torus.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm73-12-2015, author = {Emmanuel Militon}, title = {Actions of the group of homeomorphisms of the circle on surfaces}, journal = {Fundamenta Mathematicae}, volume = {233}, year = {2016}, pages = {143-172}, zbl = {06575008}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm73-12-2015} }
Emmanuel Militon. Actions of the group of homeomorphisms of the circle on surfaces. Fundamenta Mathematicae, Tome 233 (2016) pp. 143-172. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm73-12-2015/