On tame embeddings of solenoids into 3-space

• Autorzy: Boju Jiang , Shicheng Wang , Hao Zheng , Qing Zhou
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54C25: Embedding
• 37E99: None of the above, but in this section
• 57N10: Topology of general 3 -manifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 214
• Numer: 1
• Strony: 57-75

Daty

wydano

2011

Twórcy

autor

Boju Jiang

• Department of Mathematics, Peking University, Beijing 100871, China

autor

Shicheng Wang

• Department of Mathematics, Peking University, Beijing 100871, China

autor

Hao Zheng

• Department of Mathematics, Peking University, Beijing 100871, China

autor

Qing Zhou

• Department of Mathematics, East China Normal University, Shanghai 200030, China

Identyfikatory

DOI

10.4064/fm214-1-4