Constructing group actions on quasi-trees and applications to mapping class groups

By M. Bestvina, K. Bromberg, K. Fujiwara. Publications mathématiques (Bures-sur-Yvette), 2010

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Characterizations of Morse Quasi-Geodesics via Superlinear Divergence and Sublinear Contraction (2016, background): “[11] Pierre-Emmanuel Caprace and Koji Fujiwara, Rank-one isometries of buildings and quasi-morphisms of Kac-Moody groups, Geom.”
Hyperbolicities in CAT(0) cube complexes (2017, background): “In [Sis18], and in a more general form in [BBF15], it is proved that if a group G acts on a CAT(0) space X and if G contains a contracting isometry, then it is possible to construct a new action of G on a some hyperbolic space Y (in fact, a quasi-tree) such that the previous contracting isometry bec”
Growth tight actions (2014, methodology): “We recall the method of Bestvina, Bromberg, and Fujiwara [11] for producing group actions on quasi-trees.”
Asymptotic dimension and small‐cancellation for hierarchically hyperbolic spaces and groups (2015, background): “Bestvina, Bromberg and Fujiwara established finiteness of the asymptotic dimension of mapping class group [10], but without providing explicit bounds.”