No embeddings of solenoids into surfaces
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- by Boju Jiang, Shicheng Wang and Hao Zheng PDF
- Proc. Amer. Math. Soc. 136 (2008), 3697-3700 Request permission
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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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
- 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
- © Copyright 2008 American Mathematical Society
- 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
- MathSciNet review: 2415057