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Cubulating random groups at density less than $1/6$
2011
Transactions of the American Mathematical Society
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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 . Abstract. Nous prouvons que les groupes aléatoires en densité strictement inférieureà 1 6 agissent librement et cocompactement sur un complexe cubique CAT(0). De plus en densité strictement inférieureà 1 5 , ils ont un sous-groupe de codimension
doi:10.1090/s0002-9947-2011-05197-4
fatcat:zhcmkqyahzckzg73cxu2dq3lve