An Introduction to Knot Theory

Graduate Texts in Mathematics #175

by W.B. Raymond Lickorish

A selection of topics which graduate students have found to be a successful introduction to the field, employing three distinct geometric topology manoeuvres, combinatorics, and algebraic topology. Each topic is developed until significant results are achieved and each chapter ends with exercises and brief accounts of the latest research. What may reasonably be referred to as knot theory has expanded enormously over the last decade and, while the author describes important discoveries 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 intelligible style. Readers are assumed to have knowledge of the basic ideas of the fundamental group and simple homology theory, although explanations throughout the text are numerous and well-done. Written by an internationally known expert in the field, this will appeal to graduate students, mathematicians and physicists with a mathematical background wishing to gain new insights in this area.

Genres: Mathematics, Reference

214 pages, Hardcover

First published October 3, 1997

Reviews

[Saman · Rating 3 out of 5]

As the name suggests it is an introductory book (in graduate level) about knots. By knot we mean a smooth embedding of a circle in 3 dimensional space. We are interested to know if two different knots are isotopic or not (notion of equivalency), and also we are interested in topological aspects of knots, We solve such problems mostly using invariants.
Knot theory is a very important part of low dimensional topology and the study of 3 manifolds (And recently in some areas of theoretical physics).
The book covers classical invariants in knot theory like Alexander polynomial and also more modern objects like Jones and Homfly polynomials (but not homological invariants like Khovanov Homology).
The book has topological taste, full of geometric deductions and also it has lots of good problems to solve. Some chapters are even appropriate for representing to high school students and some chapters are fairly hard and advanced.