On tame embeddings of solenoids into 3-space

Boju Jiang; Shicheng Wang; Hao Zheng; Qing Zhou

Fundamenta Mathematicae (2011)

  • Volume: 214, Issue: 1, page 57-75
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Boju Jiang, et al. "On tame embeddings of solenoids into 3-space." Fundamenta Mathematicae 214.1 (2011): 57-75. <http://eudml.org/doc/283103>.

@article{BojuJiang2011,
abstract = { 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. },
author = {Boju Jiang, Shicheng Wang, Hao Zheng, Qing Zhou},
journal = {Fundamenta Mathematicae},
keywords = {solenoids; chirality; planarity; tame embeddings},
language = {eng},
number = {1},
pages = {57-75},
title = {On tame embeddings of solenoids into 3-space},
url = {http://eudml.org/doc/283103},
volume = {214},
year = {2011},
}

TY - JOUR
AU - Boju Jiang
AU - Shicheng Wang
AU - Hao Zheng
AU - Qing Zhou
TI - On tame embeddings of solenoids into 3-space
JO - Fundamenta Mathematicae
PY - 2011
VL - 214
IS - 1
SP - 57
EP - 75
AB - 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.
LA - eng
KW - solenoids; chirality; planarity; tame embeddings
UR - http://eudml.org/doc/283103
ER -

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