Knot theory is an active field of research in mathematics. In a nutshell: knot theory deals with the mathematics of embeddings of the circle in 3-space. The vast majority of the time, the underlying assumption is that the embedded circles are smooth; i. e. are the image of a smooth map of the circle into 3-space.
However, some interesting things happen when you take away the “smooth mapping” condition. Also, one can study the maps of the real line into 3-space (or into open 3-manifolds).
This blog will be about developments in this area of mathematics. I hope to start with some background material and a list of some of the more basic results; I will also talk about questions that interest me.