Chapman & Hall 2016/12
200 p. 50 illus. 24 cm
Choice Reviews 2017 August
The book gives an overview of methods to study knot projections. The intuitiveness of the objects allows us to present current research to audiences with a general mathematical background without requiring any knowledge of special (topology) courses. The book can be taken as a first approach to topology, alternative to the one given by standard text books. Exercises will be included. Nevertheless, it is mainly an introduction to an active research area, including many open questions.
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.
Table of Contents
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.