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.

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I would like permission to use one of your images in a book of my poetry; I studied Fox-Artin arcs for my PhD and published my thesis in Pacifica 1973; how do I go about it and what do I need to do for permission? Many thx, Jim McPherson

I don’t know; I think everything that I used here was “creative commons”.

I recognize your name and read some of your work as a graduate student.