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Minimal group actions on dendrites
Author(s):
Enhui
Shi;
Suhua
Wang;
Lizhen
Zhou
Journal:
Proc. Amer. Math. Soc.
138
(2010),
217-223.
MSC (2000):
Primary 37B05, 57M50
Posted:
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  acts on a nondegenerate dendrite  minimally, then  admits no  -invariant measure. In particular,  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
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:
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
Posted:
August 12, 2009
Communicated by:
Alexander N. Dranishnikov
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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