The isometry group of outer space
type: Item
instance of: scholarly article
title: The isometry group of outer space
zbMATH Open document ID: 1311.57004
author: Stefano Francaviglia
author: Armando Martino
published in: Advances in Mathematics
publication date: 2012-10-16T00:00:00Z
full work available at URL: https://arxiv.org/abs/0912.0299
review text: Royden's Theorem for Teichmüller space says that in sufficiently high genus, the isometry group of Teichmüller space with the Teichmüller metric is the extended mapping class group. The authors establish an analogue of this theorem for Culler--Vogtmann Outer Space \(CV_n\), showing that for \(n\) sufficiently large, its isometry group with the Lipschitz metric is \(\text{Out}(F_n)\). As is typical in the theory, a result analogous to one in Teichmüller theory is proven by completely different methods. The methods used in the present article concern the local structure and non--homogeneity of \(CV_n\).
reviewed by: Thomas Koberda
Mathematics Subject Classification ID: 57M07
Mathematics Subject Classification ID: 20E05
zbMATH DE Number: 6094103
zbMATH Keywords: outer space
zbMATH Keywords: free group
zbMATH Keywords: stretching factors
zbMATH Keywords: isometries
zbMATH Keywords: Lipschitz distances
MaRDI profile type: Publication
OpenAlex ID: W2015018141
arXiv ID: 0912.0299
cites work: Strongly contracting geodesics in outer space.
cites work: Asymmetry of outer space.
cites work: Automorphisms of the graph of free splittings
cites work: Train tracks and automorphisms of free groups
cites work: A remark about actions of lattices on free groups
cites work: The symmetries of outer space.
cites work: Actions of higher-rank lattices on free groups
cites work: Q3344126
cites work: Group Actions On R-Trees
cites work: Moduli of graphs and automorphisms of free groups
cites work: Geodesic currents and length compactness for automorphisms of free groups
cites work: Metric properties of outer space.
cites work: The expansion factors of an outer automorphism and its inverse
cites work: Parageometric outer automorphisms of free groups
cites work: Q4365977
cites work: THE FREQUENCY SPACE OF A FREE GROUP
cites work: Q5488879
cites work: The actions of ${\mathit{Out}(F_k)}$ on the boundary of Outer space and on the space of currents: minimal sets and equivariant incompatibility
cites work: The Patterson-Sullivan embedding and minimal volume entropy for outer space.
cites work: Q5627018
cites work: Length functions and outer space
cites work: Buildings of spherical type and finite BN-pairs
cites work: Automorphisms of free groups and outer space
cites work: Q3588176
DOI: 10.1016/J.AIM.2012.07.011
description: scientific article; zbMATH DE number 6094103