Translation equivalence in free groups
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- by Ilya Kapovich, Gilbert Levitt, Paul Schupp and Vladimir Shpilrain PDF
- Trans. Amer. Math. Soc. 359 (2007), 1527-1546 Request permission
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.References
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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
- MR Author ID: 113370
- 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
- Received by editor(s): September 17, 2004
- Received by editor(s) in revised form: January 8, 2005
- Published electronically: 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 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 1527-1546
- MSC (2000): Primary 20F36; Secondary 20E36, 57M05
- DOI: https://doi.org/10.1090/S0002-9947-06-03929-8
- MathSciNet review: 2272138