Geodesic
A dense geodesic ray in the Out$(F_r)$-quotient of reduced Outer Space
Yael Algom-Kfir1 ; Catherine Pfaff2
1University of Haifa, Israel
2University of California at Santa Barbara, USA
Groups, geometry, and dynamics, Tome 12 (2018) no. 2, pp. 571-613

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DOI

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 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.
DOI : 10.4171/ggd/449
Classification : 20-XX, 37-XX
Mots-clés : Outer automorphism group of the free group, Outer Space, geodesics

Yael Algom-Kfir  1   ; Catherine Pfaff  2

1 University of Haifa, Israel
2 University of California at Santa Barbara, USA 
Yael Algom-Kfir; Catherine Pfaff. A dense geodesic ray in the Out$(F_r)$-quotient of reduced Outer Space. Groups, geometry, and dynamics, Tome 12 (2018) no. 2, pp. 571-613. doi: 10.4171/ggd/449
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     title = {A dense geodesic ray in the {Out}$(F_r)$-quotient of reduced {Outer} {Space}},
     journal = {Groups, geometry, and dynamics},
     pages = {571--613},
     year = {2018},
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     number = {2},
     doi = {10.4171/ggd/449},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/449/}
}
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