Metric properties of outer space
Metric properties of outer space
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
1-36
Francaviglia, Stefano
91be45eb-fadf-48ed-abe8-107c65f85c6c
Martino, Armando
65f1ff81-7659-4543-8ee2-0a109be286f1
Francaviglia, Stefano
91be45eb-fadf-48ed-abe8-107c65f85c6c
Martino, Armando
65f1ff81-7659-4543-8ee2-0a109be286f1
Francaviglia, Stefano and Martino, Armando
(2008)
Metric properties of outer space.
Preprint, .
(Submitted)
Abstract
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
Text
0803.0640v2.pdf
- Author's Original
More information
Submitted date: December 2008
Identifiers
Local EPrints ID: 69568
URI: http://eprints.soton.ac.uk/id/eprint/69568
PURE UUID: 4ab52f31-c739-4066-98e8-9d0c61834f41
Catalogue record
Date deposited: 19 Nov 2009
Last modified: 14 Mar 2024 02:54
Export record
Contributors
Author:
Stefano Francaviglia
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
