Structural properties of dendrite groups

Bruno Duchesne (1) , Nicolas Monod (2)

1 IECL - Institut Élie Cartan de Lorraine
2 EPFL - Ecole Polytechnique Fédérale de Lausanne

Let G be the homeomorphism group of a dendrite. We study the normal subgroups of G. For instance, there are uncountably many non-isomorphic such groups G that are simple groups. Moreover, these groups can be chosen so that any isometric G-action on any metric space has a bounded orbit. In particular they have the fixed point property (FH).

Domaines: Théorie des groupes [math.GR]

Bruno Duchesne, Nicolas Monod. Structural properties of dendrite groups. Transactions of the American Mathematical Society, 2019, 371 (3), pp.1925-1949. ⟨10.1090/tran/7347⟩. ⟨hal-01388407v2⟩