We prove the following conjecture of J. Mycielski: There exists a free nonabelian group of piecewise linear, orientation and area preserving transformations which acts on the punctured disk {(x,y) ∈ ℝ²: 0 < x² + y² < 1} without fixed points.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm125-2-1,
author = {Grzegorz Tomkowicz},
title = {A free group of piecewise linear transformations},
journal = {Colloquium Mathematicae},
volume = {122},
year = {2011},
pages = {141-146},
zbl = {1258.03059},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm125-2-1}
}
Grzegorz Tomkowicz. A free group of piecewise linear transformations. Colloquium Mathematicae, Tome 122 (2011) pp. 141-146. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm125-2-1/