On tame embeddings of solenoids into 3-space

Details On tame embeddings of solenoids into 3-space On tame embeddings of solenoids into 3-space

2006-11-29

arxiv.org/abs/math/0611900v1

Mathematics

Geometric Topology

18 pages, 4 figures

Scientific paper

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 $\Sigma\subset \R^3$ which are strictly achiral. Since solenoids are non-planar, this contrasts sharply with the known fact that if there is a strictly achiral embedding $Y\subset \R^3$ of a compact polyhedron $Y$, then $Y$ must be planar.

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