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On regular CAT(0) cube complexes

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 نشر من قبل Nir Lazarovich
 تاريخ النشر 2014
  مجال البحث
والبحث باللغة English
 تأليف Nir Lazarovich




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We provide a necessary and sufficient condition on a finite flag simplicial complex, L, for which there exists a unique CAT(0) cube complex whose vertex links are all isomorphic to L. We then find new examples of such CAT(0) cube complexes and prove that their automorphism groups are virtually simple. The latter uses a result, which we prove in the appendix, about the simplicity of certain subgroups of the automorphism group of a rank-one CAT(0) cube complex. This result generalizes previous results by Tits and by Haglund and Paulin.



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