Geometry
On Lipschitz compactifications of trees

Presented by: Étienne Ghys

Kloeckner, Benoît1
1 Institut Fourier, université de Grenoble I, UMR 5582 CNRS–UJF, 38402 St Martin d'Hères, France
Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 413-416.

We study the Lipschitz structures on the geodesic compactification of a regular tree, that are preserved by the automorphism group. They are shown to be similar to the compactifications introduced by William Floyd, and a complete description is given.

On étudie les structures lipschitziennes portées par la compactification géodésique d'un arbre régulier, et qui sont préservées par l'action du groupe des automorphismes. On montre qu'elles sont semblables aux compactifications définies par William Floyd, et on en donne une description complète.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.02.011
Kloeckner, Benoît 1

1 Institut Fourier, université de Grenoble I, UMR 5582 CNRS–UJF, 38402 St Martin d'Hères, France 
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Kloeckner, Benoît. On Lipschitz compactifications of trees. Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 413-416. doi : 10.1016/j.crma.2008.02.011. https://www.numdam.org/articles/10.1016/j.crma.2008.02.011/

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[2] Burago, D.; Burago, Y.; Ivanov, S. A Course in Metric Geometry, Graduate Studies in Mathematics, vol. 33, American Mathematical Society, Providence, RI, 2001

[3] Floyd, W.J. Group completions and limit sets of Kleinian groups, Invent. Math., Volume 57 (1980) no. 3, pp. 205-218

[4] Kloeckner, B. On differentiable compactifications of the hyperbolic space, Transform. Groups, Volume 11 (2006) no. 2, pp. 185-194

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