Free lines for homeomorphisms of the open annulus

2006/03/09 by Lucien Guillou, Guillou, Lucien
Mathematics · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Mathematics and Applications #math.DS #msc:37E30

paper · pdf · doi:10.48550/arxiv.math/0603213

arxiv created 2006/03/09 · arxiv updated 2009/12/01

Abstract

Let H be a homeomorphism of the open annulus isotopic to the identity which admits a lift h to the plane without fixed point. We show that h admits a Brouwer line which is a lift of a properly imbedded line joining one end to the other in the annulus or H admits a free essential simple closed curve.

Related

• On the struture of homeomorphims of the open annulus
• Persistence of fixed points under rigid perturbations of maps
• Bounded homeomorphisms of the open annulus
• Three Brouwer fixed point theorems for homeomorphisms of the plane
• Homeomorphisms of the annulus with a transitive lift