Balanced walls for random groups

Abstract

We study a random group G in the Gromov density model and its Cayley complex X. For density < 5/24 we define walls in X that give rise to a nontrivial action of G on a CAT(0) cube complex. This extends a result of Ollivier and Wise, whose walls could be used only for density < 1/5. The strategy employed might be potentially extended in future to all densities < 1/4.

18 pages, 2 figures. v2: Minor improvements, final version

References in corpus (1)

• Random groups and Property (T): Żuk's theorem revisited

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