English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The question which motivates the article is the following: given a groupacting on a CAT(0) cube complex, how can we prove that it is acylindricallyhyperbolic? Keeping this goal in mind, we show a weak acylindricity of theaction on the contact graph associated to a CAT(0) cube complex, and we prove acharacterisation of WPD contracting isometries of CAT(0) cube complexes. As afirst consequence, we find alternative arguments to show several criteria whichwere proved by Indira Chatterji and Alexandre Martin. Next, we show that if agroup acts essentially and acylindrically on the hyperplanes (i.e., theintersection of the stabilisers of two hyperplanes which are sufficiently faraway from each other has its cardinality uniformly bounded) on afinite-dimensional CAT(0) cube complex, then it contains a finite-indexsubgroup which is either acylindrically hyperbolic or cyclic. Finally, we provea statement about codimension-one subgroups, which implies that, if a groupcontains a finitely generated codimension-one subgroup which is malnormal andwhich satisfies the bounded packing property, then this group must contain afinite-index subgroup which is either acylindrically hyperbolic or cyclic.

Acylindrical hyperbolicity from actions on CAT(0) cube complexes: a few criteria