Une version feuilletée équivariante du théorème de translation de Brouwer

Le Calvez, Patrice

Publications Mathématiques de l'IHÉS, Tome 102 (2005), pp. 1-98.

The Brouwer’s plane translation theorem asserts that for a fixed point free orientation preserving homeomorphism $f$ of the plane, every point belongs to a Brouwer line: a proper topological embedding C of $𝐑$, disjoint from its image and separating $f\left(C\right)$ and $f^{-1}\left(C\right)$. Suppose that $f$ commutes with the elements of a discrete group G of orientation preserving homeomorphisms acting freely and properly on the plane. We will construct a G-invariant topological foliation of the plane by Brouwer lines. We apply this result to give simple proofs of previous results about area-preserving homeomorphisms of surfaces and to prove the following theorem: any hamiltonian homeomorphism of a closed surface of genus $g\ge 1$ has infinitely many contractible periodic points.

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