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arXiv · 1610.03376

Cubulating random groups in the square model

Tomasz Odrzygóźdź
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Abstract

Our main result is that for densities $<\frac{3}{10}$ a random group in the square model has the Haagerup property and is residually finite. Moreover, we generalize the Isoperimetric Inequality, to some class of non-planar diagrams and, using this, we introduce a system of modified hypergraphs providing the structure of a space with walls on the Cayley complex of a random group. Then we show that the natural action of a random group on this space with walls is proper, which gives the proper action of a random group on a CAT(0) cube complex.

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Tomasz Odrzygóźdź. 2016-10-09. Cubulating random groups in the square model. https://arxiv.org/abs/1610.03376

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