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On tame embeddings of solenoids into 3-space

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Jiang B., Wang S., Zheng H., Zhou Q.

Fundamenta Mathematicae

2011

tom 214

nr 1

57-75

Solenoids are inverse limits of the circle, and the classical knot theory is the theory of tame embeddings of the circle into 3-space. We make a general study, including certain classification results, of tame embeddings of solenoids into 3-space, seen as the "inverse limits" of tame embeddings of the circle. Some applications in topology and in dynamics are discussed. In particular, there are tamely embedded solenoids Σ ⊂ ℝ³ 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 ⊂ ℝ³ of a compact polyhedron Y, then Y must be planar.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Jiang B.

1 Wang S.

1 Zheng H.

1 Zhou Q.

1 2011

Wyniki wyszukiwania

On tame embeddings of solenoids into 3-space