The isometry group of Outer Space
Stefano Francaviglia, Armando Martino
TL;DR
This paper proves that the isometry group of Outer Space, with respect to Lipschitz metrics, is isomorphic to the outer automorphism group of the free group, extending Royden's theorem to this setting.
Contribution
It establishes the isometry group of Outer Space as Out(F_n), providing a significant extension of Royden's theorem to Lipschitz metrics.
Findings
Isom(CV_n) is Out(F_n)
Analogues of Royden's Theorem are established for Outer Space
Lipschitz metrics are key to the analysis
Abstract
We prove analogues of Royden's Theorem for the Lipschitz metrics of Outer Space, namely that Isom(CV_n) is Out(F_n).
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