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

Yael Algom-Kfir; Catherine Pfaff

doi:10.4171/GGD/449

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

Yael Algom-Kfir, Catherine Pfaff

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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×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 language	English
Pages (from-to)	571-613
Number of pages	43
Journal	Groups, Geometry, and Dynamics
Volume	12
Issue number	2
DOIs	https://doi.org/10.4171/GGD/449
State	Published - 2018

Bibliographical note

Funding Information:
2 C. Pfaff was supported first by the ARCHIMEDE Labex (ANR-11-LABX-0033) and the A*MIDEX project (ANR-11-IDEX-0001-02) funded by the “Investissements d’Avenir,” managed by the ANR. She was secondly supported by the CRC701 grant of the DFG, supporting the projects B1 and C13 in Bielefeld.

Funding Information:
1 The research of Y. Algom-Kfir of was supported by THE ISRAEL SCIENCE FOUNDATION (grant no. 1941/14).

Publisher Copyright:
© 2018 European Mathematical Society.

Keywords

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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10.4171/GGD/449

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

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×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.",

keywords = "Geodesics, Outer Space, Outer automorphism group of the free group",

author = "Yael Algom-Kfir and Catherine Pfaff",

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year = "2018",

doi = "10.4171/GGD/449",

language = "English",

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N2 - 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.

AB - 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.

KW - Geodesics

KW - Outer Space

KW - Outer automorphism group of the free group

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JO - Groups, Geometry, and Dynamics

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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