ABSTRACT

Knot Projections offers a comprehensive overview of the latest methods in the study of this branch of topology, based on current research inspired by Arnold’s theory of plane curves, Viro’s quantization of the Arnold invariant, and Vassiliev’s theory of knots, among others. The presentation exploits the intuitiveness of knot projections to introduce the material to an audience without a prior background in topology, making the book suitable as a useful alternative to standard textbooks on the subject. However, the main aim is to serve as an introduction to an active research subject, and includes many open questions.

chapter 2|10 pages

Mathematical background (1920s)

chapter 8|14 pages

Further result of strong (1, 3) homotopy

chapter 10|22 pages

Weak (1, 2, 3) homotopy

chapter 11|22 pages

Viro’s quantization of Arnold invariant