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Abstract: The Thurston compactification of Teichmuller spaces has been generalized tomany different representation spaces by J. Morgan, P. Shalen, M. Bestvina, F.Paulin, A. Parreau and others. In the simplest case of representations offundamental groups of closed hyperbolic surfaces in PSL2,R, we prove thatthis compactification is very degenerated: the nice behaviour of the Thurstoncompactification of the Teichmuller space contrasts with wild phenomenahappening on the boundary of the other connected components of theserepresentation spaces. We prove that it is more natural to consider arefinement of this compactification, which remembers the orientation of thehyperbolic plane. The ideal points of this compactification are fat R-trees,i.e., R-trees equipped with a planar structure.



Author: Maxime Wolff

Source: https://arxiv.org/



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