Translation equivalence in free groups

Ilya Kapovich, Gilbert Levitt, Paul Schupp, Vladimir Shpilrain

Research output: Contribution to journalArticlepeer-review


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 ℝ-tree X the translation lengths of g and h on X are equal.

Original languageEnglish (US)
Pages (from-to)1527-1546
Number of pages20
JournalTransactions of the American Mathematical Society
Issue number4
StatePublished - Apr 2007
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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