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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
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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:
-
- 1.
- J. Auslander, Minimal flows and their extensions, North-Holland Mathematics Studies, 153, North-Holland, 1988. MR 956049 (89m:54050)
- 2.
- B. H. Bowditch, Hausdorff dimension and dendritic limit sets, Math. Ann. 332 (2005), 667-676. MR 2181766 (2006k:57043)
- 3.
- Y. N. Minsky, On rigidity, limit sets, and ends of hyperbolic 3-manifolds, J. Amer. Math. Soc. 7 (1994), 539-588. MR 1257060 (94m:57029)
- 4.
- J. H. Mai, E. H. Shi, The nonexistence of expansive commutative group actions on Peano continua having free dendrites, Topology Appl. 155 (2007), 33-38. MR 2363562 (2008j:37034)
- 5.
- S. B. Nadler, Jr., Continuum Theory: An Introduction, Marcel Dekker, 1992. MR 1192552 (93m:54002)
- 6.
- A. L. T. Paterson, Amenability, American Mathematical Society, Providence, RI, 1988. MR 961261 (90e:43001)
- 7.
- J. G. Ratcliffe, Foundations of hyperbolic manifolds, Grad. Texts Math., 149, Springer, 2006. MR 2249478 (2007d:57029)
- 8.
- E. H. Shi, B. Y. Sun, Fixed point properties of nilpotent group actions on 1-arcwise connected continua, Proc. Amer. Math. Soc. 137 (2009), 771-775. MR 2448600
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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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