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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
DOI: https://doi.org/10.1090/S0002-9939-08-09340-4
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 $ >1$ maps between closed oriented $ m$-manifolds can never be embedded into any closed orientable $ (m+1)$-manifold. The proof also concludes Gumerov's result on the covering of solenoids.


References [Enhancements On Off] (What's this?)

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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: https://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

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