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math.GR2016★ 6 cited
The verbal width of acylindrically hyperbolic groups is infinite
Mladen Bestvina, Ken Bromberg, Koji Fujiwara
We show that the verbal width is infinite for acylindrically hyperbolic groups, which include hyperbolic groups, mapping class groups and Out(Fn).
math.GR2010★ 28 cited
Constructing group actions on quasi-trees and applications to mapping class groups
Mladen Bestvina, Kenneth Bromberg, Koji Fujiwara
A quasi-tree is a geodesic metric space quasi-isometric to a tree. We give a general construction of many actions of groups on quasi-trees. The groups we can handle include non-ele…