Abstract
In their basic paper [C-M] Culler and Morgan emphasize the analogy between conjugacy classes of representations of a group G in SO +ℝ (2,1) = PSL(2,ℝ), and translation length functions on G which arise from (small) G-actions on ℝ-trees. It is well known that, for any finitely generated group G, an element of Hom(G, SL(2, ℂ)) is determined up to conjugation in SL(2,ℂ) by the traces of a finite set of elements of G. (See, for example, [He].) The purpose of this paper is to show that the analogue of this basic fact is not true for translation length functions of actions on ℝ-trees.
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© 1991 Springer-Verlag New York, Inc.
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Cohen, M.M., Lustig, M., Steiner, M. (1991). ℝ-Tree Actions are Not Determined by the Translation Lengths of Finitely Many Elements. In: Alperin, R.C. (eds) Arboreal Group Theory. Mathematical Sciences Research Institute Publications, vol 19. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3142-4_7
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DOI: https://doi.org/10.1007/978-1-4612-3142-4_7
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