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No embeddings of solenoids into surfaces

Author(s): Boju Jiang; Shicheng Wang; Hao Zheng
Journal: Proc. Amer. Math. Soc. 136 (2008), 3697-3700.
MSC (2000): Primary 54F15, 57N35
Posted: May 7, 2008
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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:

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Greenberg, M. J.; Harper, J. R. Algebraic topology. A first course, Mathematics Lecture Note Series 58, Benjamin/Cummings Publishing Co., Inc., Reading, MA, 1981. MR 643101 (83b:55001)

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Gumerov, R. N. On finite-sheeted covering mappings onto solenoids, Proc. Amer. Math. Soc. 133 (2005), 2771-2778. MR 2146226 (2006d:54024)

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Keesling, J.; Wilson, D. Embedding $ T\sp n$-like continua in Euclidean space. Topology Appl. 21 (1985), no. 3, 241-249. MR 812642 (87h:54033)

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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: 10.1090/S0002-9939-08-09340-4
PII: S 0002-9939(08)09340-4
Received by editor(s): November 2, 2006,
Received by editor(s) in revised form: August 9, 2007
Posted: May 7, 2008
Additional Notes: The authors were supported by an NSFC grant.
Communicated by: Alexander N. Dranishnikov
Copyright of article: Copyright 2008, American Mathematical Society

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