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 . 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.
Citation
Patrice Le Calvez. "Une nouvelle preuve du théorème de point fixe de Handel." Geom. Topol. 10 (4) 2299 - 2349, 2006. https://doi.org/10.2140/gt.2006.10.2299
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