On tame embeddings of solenoids into 3-space
Volume 214 / 2011
Fundamenta Mathematicae 214 (2011), 57-75
MSC: Primary 57N10; Secondary 37E99, 54C25.
DOI: 10.4064/fm214-1-4
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 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 \mathbb R^3 of a compact polyhedron Y, then Y must be planar.
