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Cubulating random groups at density less than 1/6

Yann Ollivier 1, 2
2 TAO - Machine Learning and Optimisation
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LRI - Laboratoire de Recherche en Informatique
Abstract : We prove that random groups at density less than 1/6 act freely and cocompactly on CAT(0) cube complexes, and that random groups at density less than 1/5 have codimension-1 subgroups. In particular, Property (T ) fails to hold at density less than 1/5.
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https://hal.archives-ouvertes.fr/hal-00858012
Contributor : Yann Ollivier <>
Submitted on : Wednesday, September 4, 2013 - 1:58:52 PM
Last modification on : Tuesday, April 21, 2020 - 1:04:32 AM

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Yann Ollivier. Cubulating random groups at density less than 1/6. Transactions of the American Mathematical Society, American Mathematical Society, 2011, 363 (9), pp.4701-4733. ⟨hal-00858012⟩

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