Mathematics – Group Theory
Scientific paper
2008-03-05
Publicacions Matem\`atiques 55(2), 2011 433-473
Mathematics
Group Theory
changelog v1 -> v2: Added an example, suggested by Bert Wiest and Thierry Coulbois showing that the symmetric metric is not ge
Scientific paper
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.
Francaviglia Stefano
Martino Armando
No associations
LandOfFree
Metric properties of Outer Space does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Metric properties of Outer Space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Metric properties of Outer Space will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-161113