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.



2 thoughts on “About

  1. 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

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