Une nouvelle preuve du theoreme de point fixe de Handel
Abstract
M Handel has proved in [Topology 38 (1999) 235--264] a fixed point theorem for an orientation preserving homeomorphism of the open unit disk, that may be extended to the closed disk and that satisfies a linking property of orbits. We give here a new proof of Handel's fixed point theorem, based on Brouwer theory and some plane topology arguments. We will slightly improve the theorem by proving the existence of a simple closed curve of index 1. This index result was known to be true under an additional hypothesis and has been used by different authors (J Franks [NYJM 2 (1996) 1--19, Trans.AMS 348 (1996) 2637--2662] S Matsumoto [Topol. Appl. 104 (2000) 191--214]) to study homeomorphisms of surfaces.
Keywords
Cite
@article{arxiv.0903.0369,
title = {Une nouvelle preuve du theoreme de point fixe de Handel},
author = {Patrice Le Calvez},
journal= {arXiv preprint arXiv:0903.0369},
year = {2009}
}
Comments
This is the version published by Geometry & Topology on 8 December 2006