Introduction to Vassiliev Knot Invariants

TL;DR

This book provides a comprehensive, accessible introduction to finite type (Vassiliev) knot invariants, emphasizing combinatorial methods and visual understanding for both beginners and advanced readers.

Contribution

It offers a clear, illustrative exposition of Vassiliev invariants, combining basic concepts with advanced topics, and serves as both a textbook and a guide to the literature.

Findings

Provides visual and combinatorial approaches to knot invariants

Bridges introductory and advanced material in knot theory

Includes illustrative examples and calculations

Abstract

This book is a detailed introduction to the theory of finite type (Vassiliev) knot invariants, with a stress on its combinatorial aspects. It is intended to serve both as a textbook for readers with no or little background in this area, and as a guide to some of the more advanced material. Our aim is to lead the reader to understanding by means of pictures and calculations, and for this reason we often prefer to convey the idea of the proof on an instructive example rather than give a complete argument. While we have made an effort to make the text reasonably self-contained, an advanced reader is sometimes referred to the original papers for the technical details of the proofs. Version 3: some typos and inaccuracies are corrected.