Asymptotic dimension and small-cancellation for hierarchically hyperbolic spaces and groups
نویسندگان
چکیده
منابع مشابه
Asymptotic Dimension and Small-cancellation for Hierarchically Hyperbolic Spaces and Groups
We prove that all hierarchically hyperbolic groups have nite asymptotic dimension. One application of this result is to obtain the sharpest known bound on the asymptotic dimension of the mapping class group of a nite type surface: improving the bound from exponential to at most quadratic in the complexity of the surface. We also apply the main result to various other hierarchically hyperbolic g...
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Suppose that a finitely generated group G is hyperbolic relative to a collection of subgroups {H1, . . . ,Hm}. We prove that if each of the subgroups H1, . . . ,Hm has finite asymptotic dimension, then asymptotic dimension of G is also finite.
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We introduce a number of tools for nding and studying hierarchically hyperbolic spaces (HHS), a rich class of spaces including mapping class groups of surfaces, Teichmüller space with either the Teichmüller or Weil-Petersson metrics, right-angled Artin groups, and the universal cover of any compact special cube complex. We begin by introducing a streamlined set of axioms de ning an HHS. We prov...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2017
ISSN: 0024-6115
DOI: 10.1112/plms.12026