Degenerations of representations and thin triangles

preprint2020arXivOpen access

Abstract

There is a compactification of the space of representations of a finitely generated group into the groups of isometries of all spaces with ΔΔ-thin triangles. The ideal points are actions on R\mathbb R-trees. It is a geometric reformulation and extension of the Culler-Morgan-Shalen theory concerning limits of representations into SL⁡(2,C)\operatorname{SL}(2,{\mathbb C}) and more generally O⁡(n,1)\operatorname{O}(n, 1). This paper was written and circulated in the early 90's, but never published.

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