Structural properties of dendrite groups

Duchesne, Bruno; Monod, Nicolas

doi:10.1090/tran/7347

Structural properties of dendrite groups
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by Bruno Duchesne and Nicolas Monod PDF

Trans. Amer. Math. Soc. 371 (2019), 1925-1949 Request permission

Abstract:

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).

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