Translation equivalence in free groups
by
Vladimir Shpilrain
The City College of New York
Coauthors: Ilya Kapovich, Gilbert Levitt, Paul Schupp

Motivated by the work on hyperbolic equivalence of homotopy classes of closed curves on surfaces, we investigate a similar phenomenon for free groups. Namely, we study the situation where 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 (or have bounded ratio). This is equivalent to the following combinatorial property: for any automorphism j of F, the cyclic lengths of j(g) and j(h) are equal (or have bounded ratio).

Date received: February 24, 2006