Chapman and Hall/CRC
200 pages | 210 B/W Illus.
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.
"Overall, this book's clear exposition makes it equally approachable to experts working in knot theory and graduate students who are just learning about the subject. It provides a comprehensive guide to current research on knot projections and different notions of equivalence along with many interesting exercises and open questions for exploration."
- Allison Henrich, Mathematical Reviews, July 2017
Introduction. Mathematical Background. A topological invariant of knot projections. Classification by RI and RII. Classification by strong and weak RIII. Constructing new topological invariants of equivalence classes of knot projections. Survey on classification problems of knot projections.