Geodesic
Locally compact lacunary hyperbolic groups
Adrien Le Boudec1 orcid
1Université Paris-Sud 11, Orsay, France
Groups, geometry, and dynamics, Tome 11 (2017) no. 2, pp. 415-454

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DOI

We investigate the class of locally compact lacunary hyperbolic groups. We prove that if a locally compact compactly generated group G admits one asymptotic cone that is a real tree and whose natural transitive isometric action is focal, then G must be a focal hyperbolic group. As an application, we characterize connected Lie groups and linear algebraic groups over an ultrametric local eld of characteristic zero having cut-points in one asymptotic cone.
DOI : 10.4171/ggd/402
Classification : 20-XX, 22-XX
Mots-clés : Lacunary hyperbolic groups, asymptotic cones, locally compact groups

Adrien Le Boudec  1

1 Université Paris-Sud 11, Orsay, France 
Adrien Le Boudec. Locally compact lacunary hyperbolic groups. Groups, geometry, and dynamics, Tome 11 (2017) no. 2, pp. 415-454. doi: 10.4171/ggd/402
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     author = {Adrien Le Boudec},
     title = {Locally compact lacunary hyperbolic groups},
     journal = {Groups, geometry, and dynamics},
     pages = {415--454},
     year = {2017},
     volume = {11},
     number = {2},
     doi = {10.4171/ggd/402},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/402/}
}
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