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A free group of piecewise linear transformations

Grzegorz Tomkowicz (2011)

Colloquium Mathematicae

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.

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