No embeddings of solenoids into surfaces

Authors:
Boju Jiang, Shicheng Wang and Hao Zheng

Journal:
Proc. Amer. Math. Soc. **136** (2008), 3697-3700

MSC (2000):
Primary 54F15, 57N35

Published electronically:
May 7, 2008

MathSciNet review:
2415057

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Abstract | References | Similar Articles | Additional Information

Abstract: A quick proof of Bing's theorem indicated by the title is given. Indeed the inverse limit of a sequence of degree maps between closed oriented -manifolds can never be embedded into any closed orientable -manifold. The proof also concludes Gumerov's result on the covering of solenoids.

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Additional Information

**Boju Jiang**

Affiliation:
Department of Mathematics, Peking University, Beijing 100871, People’s Republic of China

Email:
bjjiang@math.pku.edu.cn

**Shicheng Wang**

Affiliation:
Department of Mathematics, Peking University, Beijing 100871, People’s Republic of China

Email:
wangsc@math.pku.edu.cn

**Hao Zheng**

Affiliation:
Department of Mathematics, Zhongshan University, Guangzhou 510275, People’s Republic of China

Email:
zhenghao@sysu.edu.cn

DOI:
http://dx.doi.org/10.1090/S0002-9939-08-09340-4

Received by editor(s):
November 2, 2006

Received by editor(s) in revised form:
August 9, 2007

Published electronically:
May 7, 2008

Additional Notes:
The authors were supported by an NSFC grant.

Communicated by:
Alexander N. Dranishnikov

Article copyright:
© Copyright 2008
American Mathematical Society