No embeddings of solenoids into surfaces
Boju Jiang, Shicheng Wang, Hao Zheng
Abstract
A quick proof of Bing's theorem indicated by the title is given. The proof also concludes Gumerov's result on covering degrees of solenoids.
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No embeddings of solenoids into surfaces
Authors
Boju Jiang, Shicheng Wang, Hao Zheng
Abstract
A quick proof of Bing's theorem indicated by the title is given. The proof also concludes Gumerov's result on covering degrees of solenoids.
Paper Structure
This paper contains 3 theorems, 7 equations.
Key Result
Theorem 1
No solenoid $\Theta$ can be embedded into a surface.
Theorems & Definitions (16)
- Theorem 1
- Theorem 2
- Remark 1
- proof : Proof of Theorem \ref{['thm:non-surface']}
- proof : Proof of Theorem \ref{['thm:covering']}
- Claim 1
- proof
- Claim 2
- proof
- Claim 3
- ...and 6 more