Stefano Francaviglia, Armando Martino
Published 2008-03-05, updated 2008-12-17Version 2
We define metrics on Culler-Vogtmann space, which are an analogue of the Teichmuller 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.
Comments: changelog v1 -> v2: Added an example, suggested by Bert Wiest and Thierry Coulbois showing that the symmetric metric is not geodesic. Minor changes. Biblio updated
Journal: Publicacions Matem\`atiques 55(2), 2011 433-473
Stretching factors, metrics and train tracks for free products
Outer space for RAAGs
Limit sets of unfolding paths in Outer space
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