Cubulating random groups in the square model
Our main result is that for densities $
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| creator | Odrzygóźdź, Tomasz |
| description | Our main result is that for densities $ |
| doi_str_mv | 10.48550/arxiv.1610.03376 |
| format | Article |
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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.</description><identifier>DOI: 10.48550/arxiv.1610.03376</identifier><language>eng</language><subject>Mathematics - Geometric Topology ; Mathematics - Group Theory</subject><creationdate>2016-10</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1610.03376$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1610.03376$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Odrzygóźdź, Tomasz</creatorcontrib><title>Cubulating random groups in the square model</title><description>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
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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.</abstract><doi>10.48550/arxiv.1610.03376</doi><oa>free_for_read</oa></addata></record> |
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| source | arXiv.org |
| subjects | Mathematics - Geometric Topology Mathematics - Group Theory |
| title | Cubulating random groups in the square model |
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