Une version feuilletée équivariante du théorème de translation de Brouwer
Publications Mathématiques de l'IHÉS, Volume 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(C) and f -1 (C). 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 g1 has infinitely many contractible periodic points.

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     author = {Le Calvez, Patrice},
     title = {Une version feuillet\'ee \'equivariante du th\'eor\`eme de translation de {Brouwer}},
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Le Calvez, Patrice. Une version feuilletée équivariante du théorème de translation de Brouwer. Publications Mathématiques de l'IHÉS, Volume 102 (2005), pp. 1-98. doi : 10.1007/s10240-005-0034-1. http://archive.numdam.org/articles/10.1007/s10240-005-0034-1/

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