The FN-action on the Product of the Two Limit Trees for an Iwip Automorphism
An elementary proof is given for the fact that, for every non-surface iwip automorphisms ϕ of a free group F N , the F N -action, on the cartesian product T+(ϕ) × T+(ϕ −1) of the (non-simplicial) forward limit ℝ-trees for ϕ and ϕ −1, is properly discontinuous. Alternative proofs, derived from deeper results, have been given by Bestvina-Feighn-Handel  and later by Levitt-Lustig ; compare also Guirardel .
Mathematics Subject Classification (2000)Primary 20F36 Secondary 20E36 57M05
Keywordsℝ-trees discrete action on product iwip automorphisms of free groups
Unable to display preview. Download preview PDF.
- M. Bestvina and M. Feighn, Outer limits, preprint 1992Google Scholar
- M. Culler, G. Levitt, P. Shalen, unpublished manuscriptGoogle Scholar
- G. Levitt and M. Lustig, Automorphisms of free groups have asymtotically periodic dynamics, to appear in J. reine u. angew. Math. (arXiv math. GR 0407437)Google Scholar
- M. Lustig, Automorphismen von freien Gruppen, Habilitationsschrift 1992, Ruhr-Universität BochumGoogle Scholar
- M. Lustig, Discrete actions on the product of two non-simplicialℝ-trees, preprint 1994Google Scholar
- M. Lustig et al., Seven steps to happiness, preliminary preprint 2008Google Scholar