Equivariant embeddings of trees into hyperbolic spaces
By M. Burger, A. Iozzi, Nicolas Monod. 2004
53 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d80a4e68bf67b2957e8ab8c0451df800b573f082
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In Computational Theory and Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Superrigidity for irreducible lattices and geometric splitting (2005, background): “s: 18.Example.If Xis a Hilbert space, then Tc and Tw both coincide with the weak topology. 19. Example.If X is the standard infinite-dimensional (separable) real hyperbolic space O(1,∞)/O(∞) (see e.g. [BIM]), then Tw and Tc coincide; moreover, they are induced from the weak topology if we realize Xwi”
- Dynamical degrees of birational transformations of projective surfaces (2013, background): “When the infimum is not realized, L(g) is equal to 0, and g is parabolic: It fixes a unique line in the isotropic cone of ZX ; this line is fixed pointwise, and all orbits g(x) in HX accumulate to the corresponding boundary point when n goes to ±∞ (see [14] for examples of accumulation without conve”