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Translation equivalence in free groups

Author(s): Ilya Kapovich; Gilbert Levitt; Paul Schupp; Vladimir Shpilrain
Journal: Trans. Amer. Math. Soc. 359 (2007), 1527-1546.
MSC (2000): Primary 20F36; Secondary 20E36, 57M05
Posted: October 16, 2006
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Abstract: 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.

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Additional Information:

Ilya Kapovich
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois 61801
Email: kapovich@math.uiuc.edu

Gilbert Levitt
Affiliation: Laboratoire de Mathematiques Nicolas Oresme, CNRS UMR 6139, Universite de Caen, BP 5186, 14032 Caen Cedex, France
Email: Gilbert.Levitt@math.unicaen.fr

Paul Schupp
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois 61801
Email: schupp@math.uiuc.edu

Vladimir Shpilrain
Affiliation: Department of Mathematics, The City College of New York, New York, New York 10031
Email: shpil@groups.sci.ccny.cuny.edu

DOI: 10.1090/S0002-9947-06-03929-8
PII: S 0002-9947(06)03929-8
Received by editor(s): September 17, 2004
Received by editor(s) in revised form: January 8, 2005
Posted: October 16, 2006
Additional Notes: The first author acknowledges the support of the Max Planck Institute of Mathematics in Bonn. The first and the third authors were supported by NSF grant DMS\#0404991 and NSA grant DMA\#H98230-04-1-0115. The fourth author was supported by NSF grant DMS\#0405105
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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