Convex cores for actions on finite-rank median algebras
[Cœurs convexes pour les actions sur les algèbres médianes de rang fini]
Fioravanti, Elia1
1 Max Planck Institute for Mathematics, Bonn (Germany)
Annales de l'Institut Fourier, Online first, 48 p.

Nous montrons que chaque action d’un groupe fini généré sur une algèbre médiane de rang fini admet un «  cœur convexe  » non vide, même en l’absence de métrique ou de topologie donnée. Nous utilisons ensuite cela pour déduire un analogue du théorème du tore plat pour les actions sur des espaces médians connectés de rang fini. Nous prouvons également que les isométries des espaces médians connectés de rang fini sont soit elliptiques, soit loxodromiques.

We show that every action of a finitely generated group on a finite-rank median algebra admits a nonempty “convex core”, even when no metric or topology is given. We then use this to deduce an analogue of the flat torus theorem for actions on connected finite-rank median spaces. We also prove that isometries of connected finite-rank median spaces are either elliptic or loxodromic.

Reçu le :
Révisé le :
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Première publication :
DOI : 10.5802/aif.3609
Classification : 20F65, 20F67, 22F50
Keywords: Median algebra, median space, semisimple, flat torus, convex core.
Mot clés : Algèbre médiane, espace médian, semi-simple, tore plat, cœur convexe.
Fioravanti, Elia 1

1 Max Planck Institute for Mathematics, Bonn (Germany) 
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Fioravanti, Elia. Convex cores for actions on finite-rank median algebras. Annales de l'Institut Fourier, Online first, 48 p.

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