Une version feuilletée équivariante du théorème de translation de Brouwer

Patrice Le Calvez

Publications Mathématiques de l'IHÉS (2005)

  • Volume: 102, page 1-98
  • ISSN: 0073-8301


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.

How to cite


Le Calvez, Patrice. "Une version feuilletée équivariante du théorème de translation de Brouwer." Publications Mathématiques de l'IHÉS 102 (2005): 1-98. <http://eudml.org/doc/104214>.

author = {Le Calvez, Patrice},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {Brouwer's plan translation theorem; Brouwer line; Brouwer homeomorphism; foliation; area-preserving homeomorphism; orientation preserving homeomorphism},
language = {fre},
pages = {1-98},
publisher = {Springer},
title = {Une version feuilletée équivariante du théorème de translation de Brouwer},
url = {http://eudml.org/doc/104214},
volume = {102},
year = {2005},

AU - Le Calvez, Patrice
TI - Une version feuilletée équivariante du théorème de translation de Brouwer
JO - Publications Mathématiques de l'IHÉS
PY - 2005
PB - Springer
VL - 102
SP - 1
EP - 98
LA - fre
KW - Brouwer's plan translation theorem; Brouwer line; Brouwer homeomorphism; foliation; area-preserving homeomorphism; orientation preserving homeomorphism
UR - http://eudml.org/doc/104214
ER -


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