METRIC PROPERTIES OF OUTER SPACE

By S. Francaviglia, Armando Martino. 2008

98 citations recorded by the source corpus.

We define metrics on Culler-Vogtmann space, which are an analogue of the Thurston metric and are constructed using stretching factors. In fact the metrics we study are related, one being a symmetrised version of the other. We investigate the basic properties of these metrics, showing the advantages and pathologies of both choices. We show how to compute stretching factors between marked metric graphs in an easy way and we discuss the behaviour of stretching factors under iterations of automorphisms. We study metric properties of folding paths, showing that they are geodesic for the non-symmetric metric and, if they do not enter the thin part of Outer Space, quasi-geodesic for the symmetric metric.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/48adb83e3020a7ca4a124874ec264dc3006e843b

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Asymmetry of Outer space (2009, methodology): “ Thurston’s Lipschitz metric [Thu]. It is only the latter one that has an analog in Outer space. The ﬁrst systematic study of the Lipschitz metric in Outer space was conducted by Francaviglia-Martino [FM]. Just like Thurston’s metric, this metric is not symmetric, but it does have many useful proper”
Hyperbolicity of the complex of free factors (2011, background): “This is the approach taken in [11], to which the reader is referred for further discussion.”
The co‐surface graph and the geometry of hyperbolic free group extensions (2016, methodology): “With this notation we have the following useful formula for the metric [16]:”
Hyperbolic extensions of free groups (2014, methodology): “The folding paths used this paper, as deﬁned above, are sometimes called “greedy folding paths” [BF2] or “fast folding lines” [FM2] in the literature.”