On tame embeddings of solenoids into 3-space

DOI10.4064/FM214-1-4zbMATH Open1260.57037arXivmath/0611900OpenAlexW2018587826MaRDI QIDQ3174481

Shicheng Wang, Qing Zhou, Hao Zheng, Boju Jiang

Publication date: 14 October 2011

Published in: Fundamenta Mathematicae (Search for Journal in Brave)

Abstract: Solenoids are ``inverse limits of the circle, and the classical knot theory is the theory of tame embeddings of the circle into the 3-space. We give some general study, including certain classification results, of tame embeddings of solenoids into the 3-space as the ``inverse limits of the tame embeddings of the circle. Some applications are discussed. In particular, there are ``tamely embedded solenoids $Sigmasubset{R}^3$ which are strictly achiral. Since solenoids are non-planar, this contrasts sharply with the known fact that if there is a strictly achiral embedding $Ysubset{R}^3$ of a compact polyhedron $Y$, then $Y$ must be planar.

Full work available at URL: https://arxiv.org/abs/math/0611900

zbMATH Keywords

planaritysolenoidschiralitytame embeddings

Mathematics Subject Classification ID

Embedding (54C25) Low-dimensional dynamical systems (37E99)

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