Geodesic
Une version feuilletée équivariante du théorème de translation de Brouwer
Publications Mathématiques de l'IHÉS, Tome 102 (2005), pp. 1-98

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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 g≥1 has infinitely many contractible periodic points.

@article{PMIHES_2005__102__1_0,
     author = {Le Calvez, Patrice},
     title = {Une version feuillet\'ee \'equivariante du th\'eor\`eme de translation de {Brouwer}},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {1--98},
     publisher = {Springer},
     volume = {102},
     year = {2005},
     doi = {10.1007/s10240-005-0034-1},
     mrnumber = {2217051},
     zbl = {1152.37015},
     language = {fr},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-005-0034-1/}
}
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Le Calvez, Patrice. Une version feuilletée équivariante du théorème de translation de Brouwer. Publications Mathématiques de l'IHÉS, Tome 102 (2005), pp. 1-98. doi: 10.1007/s10240-005-0034-1

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