Resumen de Metric properties of Outer Space

Stefano Francaviglia, Armando Martino

• We define metrics on Culler-Vogtmann space, which are an ana- logue of the Thurston metric and are constructed using stretching factors. In fact the metrics we study are related, one being a sym- metrised 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 met- ric graphs in an easy way and we discuss the behaviour of stretch- ing 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.