2011
DOI: 10.1007/s10711-011-9591-2
|View full text |Cite
|
Sign up to set email alerts
|

Asymmetry of Outer space

Abstract: We study the asymmetry of the Lipschitz metric d on Outer space. We introduce an (asymmetric) Finsler norm · L that induces d. There is an Out (F n )-invariant "potential" defined on Outer space such that when · L is corrected by d , the resulting norm is quasi-symmetric. As an application, we give new proofs of two theorems of Handel-Mosher, that d is quasi-symmetric when restricted to a thick part of Outer space, and that there is a uniform bound, depending only on the rank, on the ratio of logs of growth ra… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

0
41
0

Year Published

2012
2012
2021
2021

Publication Types

Select...
8

Relationship

2
6

Authors

Journals

citations
Cited by 33 publications
(41 citation statements)
references
References 6 publications
0
41
0
Order By: Relevance
“…. , |x k |} are vector norms i.e., they satisfy the following axioms: (1) x p 0 with equality if and only if x = 0; (2) μx p = |μ| x p ; and (3) x + y p x p + y p . Let us extend these notions to the non-abelian context, via the length function.…”
Section: The P-norm Of An Automorphismmentioning
confidence: 99%
See 2 more Smart Citations
“…. , |x k |} are vector norms i.e., they satisfy the following axioms: (1) x p 0 with equality if and only if x = 0; (2) μx p = |μ| x p ; and (3) x + y p x p + y p . Let us extend these notions to the non-abelian context, via the length function.…”
Section: The P-norm Of An Automorphismmentioning
confidence: 99%
“…This can be expressed in the following useful way: Lemma 2.6 For every ϕ ∈ Aut F r , ϕ 1 [ϕ] 1 ϕ ab 1 , with equalities if and only if, for every i = 1, . .…”
Section: Abelianizationmentioning
confidence: 99%
See 1 more Smart Citation
“…2 ) is the graph corresponding to T 1 (resp. T 2 ) in outer space, ie its quotient by Let e be an oriented edge of 1 . Subdivide e into e C e , and let p e be the subdivision point.…”
Section: Actions On Trees and Guirardel's Intersection Numbermentioning
confidence: 99%
“…Its only failure to be a distance is that it is not symmetric; it is not hard to construct examples of [2]). In spite of this anomaly, we will refer to d L as the Lipschitz metric on CV k .…”
Section: Preliminariesmentioning
confidence: 99%