A free group of piecewise linear transformations
Volume 125 / 2011
Colloquium Mathematicum 125 (2011), 141-146
MSC: Primary 03E05, 20E05, 51M05; Secondary 20G20.
DOI: 10.4064/cm125-2-1
Abstract
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 $\{(x,y) \in{ \mathbb{R}^{2}} : 0 < x^{2}+y^{2} < 1\}$ without fixed points.
