JournalsggdVol. 12, No. 2pp. 571–613

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

  • Yael Algom-Kfir

    University of Haifa, Israel
  • Catherine Pfaff

    University of California at Santa Barbara, USA
A dense geodesic ray in the Out$(F_r)$-quotient of reduced Outer Space cover
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Abstract

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×mm \times m matrices is dense in the positive cone R+m\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.

Cite this article

Yael Algom-Kfir, Catherine Pfaff, A dense geodesic ray in the Out(Fr)(F_r)-quotient of reduced Outer Space. Groups Geom. Dyn. 12 (2018), no. 2, pp. 571–613

DOI 10.4171/GGD/449