A dense geodesic ray in the Out(F_r)-quotient of reduced Outer Space

2015/08/23 by Yael Algom-Kfir, Algom-Kfir, Yael, Catherine Pfaff +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.DS #math.GR #math.GT

paper · pdf · doi:10.48550/arxiv.1508.05622

arxiv created 2016/06/03 · arxiv updated 2016/06/07

Abstract

In 1981 Masur proved the existence of a dense geodesic in the moduli space for a Teichmüller space. We prove an analogue theorem for reduced Outer Space endowed with the Lipschitz metric. We also prove two results possibly of independent interest: we show Brun's unordered algorithm weakly converges and from this prove that the set of Perron-Frobenius eigenvectors of positive integer m × m matrices is dense in the positive cone ℝ^m₊ (these matrices will in fact be the transition matrices of positive automorphisms). We give a proof in the appendix that not every point in the boundary of Outer Space is the limit of a flow line.

Related

• Divergent geodesics in the Universal Teichmüller space
• Stable Strata of Geodesics in Outer Space
• Visual sphere and Thurston's boundary of the Universal Teichmüller space
• Masur's criterion does not hold in the Thurston metric
• Bounded geodesics in moduli space