No embeddings of solenoids into surfaces

Jiang, Boju; Wang, Shicheng; Zheng, Hao

doi:10.1090/S0002-9939-08-09340-4

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.

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