Lipschitz metric on outer space

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Publication Type dissertation
School or College College of Science
Department Mathematics
Author Algom-Kfir, Yael
Title Lipschitz metric on outer space
Date 2010-05
Description In 1986 Culler and Vogtmann invented a topological space, which later became known as Outer Space, to serve as a topological model for the group Out(Fn), the outer automorphism group of the free group of rank n. Recently, attempts have been made to endow Outer Space with a metric so as to make it a geodesic space on which Out(Fn) acts by isometries. One immediately encounters some obstacles because of certain nonsymmetric phenomena which occur in Out(Fn). This work is concerned with investigating the properties of the Lipschitz metric, an asymmetric metric on Outer Space. We prove two main theorems: - the Asymmetry Theorem, which investigates how d(x; y) and d(y; x) might di er. This is joint work with Mladen Bestvina. - the Contracting Geodesics Theorem, which shows that Outer Space is negatively curved in certain directions. We remark that Outer Space has been shown by Bridson and Vogtmann not to admit a ?-hyperbolic or a CAT(0) metric. In addition to proving these theorems we describe their signi cance and prove some applications.
Type Text
Publisher University of Utah
Subject Geometry; Outer Space; Lipschitz metric; Asymmetry theorem; Contracting geodesics theorem
Subject LCSH Lipschitz spaces; Topological spaces
Dissertation Institution University of Utah
Dissertation Name PhD
Language eng
Rights Management ©Yael Algom-Kfir
Format Medium application/pdf
Format Extent 579-829 bytes
Identifier us-etd2,152218
Source Original in Marriott Library Special Collections, QA3.5 2010 .A43
ARK ark:/87278/s6xw50g1
Setname ir_etd
ID 193879
Reference URL https://collections.lib.utah.edu/ark:/87278/s6xw50g1