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

In 1981 Masur proved the existence of a dense geodesic in the moduli space for a Teichm\"uller 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 weakl...

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Bibliographic Details
Published in:arXiv.org 2016-06
Main Authors: Algom-Kfir, Yael, Pfaff, Catherine
Format: Article
Language:English
Subjects:
Algorithms
Automorphisms
Eigenvectors
Online Access:Get full text
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Summary:In 1981 Masur proved the existence of a dense geodesic in the moduli space for a Teichm\"uller 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 \(m \times m\) matrices is dense in the positive cone \(\mathbb{R}^m_+\) (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.
ISSN:2331-8422