Minimal group actions on dendrites

Shi, Enhui; Wang, Suhua; Zhou, Lizhen

doi:10.1090/S0002-9939-09-10000-X

Minimal group actions on dendrites
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by Enhui Shi, Suhua Wang and Lizhen Zhou PDF

Proc. Amer. Math. Soc. 138 (2010), 217-223 Request permission

Abstract:

Minimal group actions on dendrites appear naturally in the study of 3-dimensional hyperbolic geometry. In this paper, it is shown that if a group $G$ acts on a nondegenerate dendrite $X$ minimally, then $X$ admits no $G$-invariant measure. In particular, $G$ cannot be amenable.

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