Une nouvelle preuve du theoreme de point fixe de Handel

Patrice Le Calvez

doi:10.2140/gt.2006.10.2299

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arXiv · 0903.0369

Une nouvelle preuve du theoreme de point fixe de Handel

Patrice Le Calvez

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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.

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Patrice Le Calvez. 2009-03-02. Une nouvelle preuve du theoreme de point fixe de Handel. https://doi.org/10.2140/gt.2006.10.2299

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