An introduction to knot theory

by W. B. Raymond Lickorish

This volume is an introduction to mathematical knot theory - the theory of knots and links of simple closed curves in three-dimensional space. It consists of a selection of topics that graduate students have found to be a successful introduction to the field. Three distinct techniques are employed: geometric topology manoeuvres; combinatorics; and algebraic topology. Each topic is developed until significant results are achieved, and chapters end with exercises and brief accounts of state-of-the-art research. What may reasonably be referred to as knot theory has expanded enormously over the last decade, and while the author describes important discoveries from throughout the twentieth century, the latest discoveries such as quantum invariants of 3-manifolds - as well as generalisations and applications of the Jones polynomial - are also included, presented in an easily understandable style. Thus, this constitutes a comprehensive introduction to the field, presenting modern developments