Acylindrical actions on projection complexes

Mladen Bestvina; Kenneth Bromberg; Koji Fujiwara; Alessandro Sisto

doi:10.4171/lem/65-1/2-1

JournalslemVol. 65, No. 1/2pp. 1–32

Acylindrical actions on projection complexes

Mladen Bestvina
University of Utah, Salt Lake City, USA
Kenneth Bromberg
University of Utah, Salt Lake City, USA
- MathSciNet
- zbMATH Open
Koji Fujiwara
Kyoto University, Japan
- MathSciNet
- zbMATH Open
Alessandro Sisto
ETH Zürich, Switzerland

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Abstract

We simplify the construction of projection complexes from [BBF2]. To do so, we introduce a sharper version of the Behrstock inequality, and show that it can always be enforced. Furthermore, we use the new setup to prove acylindricity results for the action on the projection complexes.

We also treat quasi-trees of metric spaces associated to projection complexes, and prove an acylindricity criterion in that context as well.

Cite this article

Mladen Bestvina, Kenneth Bromberg, Koji Fujiwara, Alessandro Sisto, Acylindrical actions on projection complexes. Enseign. Math. 65 (2019), no. 1/2, pp. 1–32

DOI 10.4171/LEM/65-1/2-1