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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Minimal group actions on dendrites


Authors: Enhui Shi, Suhua Wang and Lizhen Zhou
Journal: Proc. Amer. Math. Soc. 138 (2010), 217-223
MSC (2000): Primary 37B05, 57M50
Published electronically: August 12, 2009
MathSciNet review: 2550186
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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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Additional Information

Enhui Shi
Affiliation: Department of Mathematics, Soochow University, No. 1 Shizi Street, Suzhou 215006, People’s Republic of China
Email: ehshi@yahoo.cn

Suhua Wang
Affiliation: Department of Mathematics, Soochow University, No. 1 Shizi Street, Suzhou 215006, People’s Republic of China
Email: wangsuhuasz@yahoo.com.cn

Lizhen Zhou
Affiliation: Department of Mathematics, Soochow University, No. 1 Shizi Street, Suzhou 215006, People’s Republic of China
Email: zhoulizhen@suda.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10000-X
PII: S 0002-9939(09)10000-X
Keywords: Dendrite, minimal group action, amenable group, invariant measure, weak mixing
Received by editor(s): November 23, 2008
Received by editor(s) in revised form: April 10, 2009, and April 14, 2009
Published electronically: August 12, 2009
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.