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Cubulating random groups in the square model

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Abstract

Our main result is that for densities < 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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Authors and Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656, Warsaw, Poland

    Tomasz Odrzygóźdź

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  1. Tomasz Odrzygóźdź
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Correspondence to Tomasz Odrzygóźdź.

Additional information

The author was partially supported by Polish National Science Center grant UMO- 2015/18/M/ST1/00050, NSERC and Polish Academy of Sciences.

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Odrzygóźdź, T. Cubulating random groups in the square model. Isr. J. Math. 227, 623–661 (2018). https://doi.org/10.1007/s11856-018-1734-9

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  • DOI: https://doi.org/10.1007/s11856-018-1734-9

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