A free group of piecewise linear transformations

Volume 125 / 2011

Grzegorz Tomkowicz Colloquium Mathematicum 125 (2011), 141-146 MSC: Primary 03E05, 20E05, 51M05; Secondary 20G20. DOI: 10.4064/cm125-2-1


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.


  • Grzegorz TomkowiczCentrum Edukacji $G^2$
    Moniuszki 9
    41-902 Bytom, Poland

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