Equivariant embeddings of trees into hyperbolic spaces

Details Equivariant embeddings of trees into hyperbolic spaces Equivariant embeddings of trees into hyperbolic spaces

2004-04-29

arxiv.org/abs/math/0404530v3

Mathematics

Group Theory

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Scientific paper

We study isometric actions of tree automorphism groups on the infinite-dimensional hyperbolic spaces. On the one hand, we exhibit a general one-parameter family of such representations and analyse the corresponding equivariant embeddings of the trees, showing that they are convex-cocompact and asymptotically isometric. On the other hand, focusing on the case of sufficiently transitive groups of automorphisms of locally finite trees, we classify completely all irreducible representations by isometries of hyperbolic spaces. It turns out that in this case our one-parameter family exhausts all non-elementary representations.

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