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Small cancellation in acylindrically hyperbolic groups

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 نشر من قبل Michael Hull
 تاريخ النشر 2013
  مجال البحث
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 تأليف M. Hull




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We generalize a version of small cancellation theory to the class of acylindrically hyperbolic groups. This class contains many groups which admit some natural action on a hyperbolic space, including non-elementary hyperbolic and relatively hyperbolic groups, mapping class groups, and groups of outer automorphisms of free groups. Several applications of this small cancellation theory are given, including to Frattini subgroups and Kazhdan constants, the construction of various exotic quotients, and to approximating acylindrically hyperbolic groups in the topology of marked group presentations.



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