Une nouvelle preuve du theoreme de point fixe de Handel

Details Une nouvelle preuve du theoreme de point fixe de Handel Une nouvelle preuve du theoreme de point fixe de Handel

2009-03-02

arxiv.org/abs/0903.0369v1

Geom. Topol. 10 (2006) 2299-2349

Mathematics

Geometric Topology

This is the version published by Geometry & Topology on 8 December 2006

Scientific paper

10.2140/gt.2006.10.2299

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.

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