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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm214-1-4,
author = {Boju Jiang and Shicheng Wang and Hao Zheng and Qing Zhou},
title = {On tame embeddings of solenoids into 3-space},
journal = {Fundamenta Mathematicae},
volume = {215},
year = {2011},
pages = {57-75},
zbl = {1260.57037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm214-1-4}
}
Boju Jiang; Shicheng Wang; Hao Zheng; Qing Zhou. On tame embeddings of solenoids into 3-space. Fundamenta Mathematicae, Tome 215 (2011) pp. 57-75. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm214-1-4/