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Mathematics > Group Theory

arXiv:math/0404530 (math)
[Submitted on 29 Apr 2004 (v1), last revised 17 Jul 2004 (this version, v3)]

Title:Equivariant embeddings of trees into hyperbolic spaces

Authors:M. Burger, A. Iozzi, N. Monod
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Abstract: 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.
Comments: Added two references
Subjects: Group Theory (math.GR); Geometric Topology (math.GT); Metric Geometry (math.MG)
Cite as: arXiv:math/0404530 [math.GR]
  (or arXiv:math/0404530v3 [math.GR] for this version)
  https://doi.org/10.48550/arXiv.math/0404530
Journal reference: IMRN 2005:22 (2005), 1331--1369
Related DOI: https://doi.org/10.1155/IMRN.2005.1331

Submission history

From: Nicolas Monod [view email]
[v1] Thu, 29 Apr 2004 15:12:58 UTC (32 KB)
[v2] Thu, 29 Apr 2004 20:02:00 UTC (32 KB)
[v3] Sat, 17 Jul 2004 17:47:44 UTC (32 KB)
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