Geodesic
Small cancellation in acylindrically hyperbolic groups
Michael Hull1
1University of Illinois-Urbana Champaign, USA
Groups, geometry, and dynamics, Tome 10 (2016) no. 4, pp. 1077-1119

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DOI

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.
DOI : 10.4171/ggd/377
Classification : 20-XX
Mots-clés : Small cancellation theory, acylindrically hyperbolic groups

Michael Hull  1

1 University of Illinois-Urbana Champaign, USA 
Michael Hull. Small cancellation in acylindrically hyperbolic groups. Groups, geometry, and dynamics, Tome 10 (2016) no. 4, pp. 1077-1119. doi: 10.4171/ggd/377
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     author = {Michael Hull},
     title = {Small cancellation in acylindrically hyperbolic groups},
     journal = {Groups, geometry, and dynamics},
     pages = {1077--1119},
     year = {2016},
     volume = {10},
     number = {4},
     doi = {10.4171/ggd/377},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/377/}
}
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