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.References
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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
- MR Author ID: 710093
- 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
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 217-223
- MSC (2000): Primary 37B05, 57M50
- DOI: https://doi.org/10.1090/S0002-9939-09-10000-X
- MathSciNet review: 2550186