Knot Projections

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.

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.

Noboru Ito is currently a project researcher at the University of Tokyo, Japan. He was previously an assistant professor and associate professor of Mathematics at the Waseda Institute for Advanced Study, in Tokyo, Japan.