Strongly contracting geodesics in Outer Space

Yael Algom-Kfir

doi:10.2140/gt.2011.15.2181

Strongly contracting geodesics in Outer Space

Research output: Contribution to journal › Article › peer-review

Abstract

We study the Lipschitz metric on Outer Space and prove that fully irreducible elements of Out(F_n) act by hyperbolic isometries with axes which are strongly contracting. As a corollary, we prove that the axes of fully irreducible automorphisms in the Cayley graph of Out(F_n) are Morse, meaning that a quasi-geodesic with endpoints on the axis stays within a bounded distance from the axis.

Original language	English
Pages (from-to)	2181-2233
Number of pages	53
Journal	Geometry and Topology
Volume	15
Issue number	4
DOIs	https://doi.org/10.2140/gt.2011.15.2181
State	Published - 2011
Externally published	Yes

ASJC Scopus subject areas

Geometry and Topology

Access to Document

10.2140/gt.2011.15.2181

Cite this

@article{1b9025f09e1344a0854cf5bb3a468b58,

title = "Strongly contracting geodesics in Outer Space",

abstract = "We study the Lipschitz metric on Outer Space and prove that fully irreducible elements of Out(Fn) act by hyperbolic isometries with axes which are strongly contracting. As a corollary, we prove that the axes of fully irreducible automorphisms in the Cayley graph of Out(Fn) are Morse, meaning that a quasi-geodesic with endpoints on the axis stays within a bounded distance from the axis.",

author = "Yael Algom-Kfir",

year = "2011",

doi = "10.2140/gt.2011.15.2181",

language = "English",

volume = "15",

pages = "2181--2233",

journal = "Geometry and Topology",

issn = "1465-3060",

publisher = "Mathematical Sciences Publishers",

number = "4",

}

TY - JOUR

T1 - Strongly contracting geodesics in Outer Space

AU - Algom-Kfir, Yael

PY - 2011

Y1 - 2011

N2 - We study the Lipschitz metric on Outer Space and prove that fully irreducible elements of Out(Fn) act by hyperbolic isometries with axes which are strongly contracting. As a corollary, we prove that the axes of fully irreducible automorphisms in the Cayley graph of Out(Fn) are Morse, meaning that a quasi-geodesic with endpoints on the axis stays within a bounded distance from the axis.

AB - We study the Lipschitz metric on Outer Space and prove that fully irreducible elements of Out(Fn) act by hyperbolic isometries with axes which are strongly contracting. As a corollary, we prove that the axes of fully irreducible automorphisms in the Cayley graph of Out(Fn) are Morse, meaning that a quasi-geodesic with endpoints on the axis stays within a bounded distance from the axis.

UR - http://www.scopus.com/inward/record.url?scp=82955188696&partnerID=8YFLogxK

U2 - 10.2140/gt.2011.15.2181

DO - 10.2140/gt.2011.15.2181

M3 - Article

AN - SCOPUS:82955188696

SN - 1465-3060

VL - 15

SP - 2181

EP - 2233

JO - Geometry and Topology

JF - Geometry and Topology

IS - 4

ER -

Strongly contracting geodesics in Outer Space

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this