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Article Dans Une Revue Michigan Mathematical Journal Année : 2002

Median sets of isometries in CAT(0) cube complexes and some applications

Résumé

In this article, we associate to isometries of CAT(0) cube complexes specific subspaces, referred to as \emph{median sets}, which play a similar role as minimising sets of semisimple isometries in CAT(0) spaces. Various applications are deduced, including a cubulation of centralisers, a splitting theorem, a proof that Dehn twists in mapping class groups must be elliptic for every action on a CAT(0) cube complex, a cubical version of the flat torus theorem, and a structural theorem about polycyclic groups acting on CAT(0) cube complexes.

Dates et versions

hal-03806597 , version 1 (07-10-2022)

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Anthony Genevois. Median sets of isometries in CAT(0) cube complexes and some applications. Michigan Mathematical Journal, 2002, ⟨10.1307/mmj/20195823⟩. ⟨hal-03806597⟩
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