Translation equivalence in free groups

Motivated by the work of Leininger on hyperbolic equivalence of homotopy classes of closed curves on surfaces, we investigate a similar phenomenon for free groups. Namely, we study the situation when two elements g,h in a free group F have the property that for every free isometric action of F on an...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2007-04, Vol.359 (4), p.1527-1546
Main Authors: Kapovich, Ilya, Levitt, Gilbert, Schupp, Paul, Shpilrain, Vladimir
Format: Article
Language:English
Subjects:
Algebra
Algebraic conjugates
Automorphisms
Closed curves
Equivalence relation
Exact sciences and technology
Group theory
Group theory and generalizations
Integers
Laminates
Manifolds and cell complexes
Mathematical theorems
Mathematics
Sciences and techniques of general use
Topology
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:Motivated by the work of Leininger on hyperbolic equivalence of homotopy classes of closed curves on surfaces, we investigate a similar phenomenon for free groups. Namely, we study the situation when two elements g,h in a free group F have the property that for every free isometric action of F on an \mathbb{R}-tree X the translation lengths of g and h on X are equal.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-06-03929-8