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

Yael Algom-Kfir, Catherine Pfaff

Research output: Contribution to journalArticlepeer-review


In [16] Masur proved the existence of a dense geodesic in the moduli space for a surface. 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 Rm C (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.

Original languageEnglish
Pages (from-to)571-613
Number of pages43
JournalGroups, Geometry, and Dynamics
Issue number2
StatePublished - 2018

Bibliographical note

Publisher Copyright:
© 2018 European Mathematical Society.


  • Geodesics
  • Outer Space
  • Outer automorphism group of the free group

ASJC Scopus subject areas

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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