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Full Description
This book is an elementary introduction to knot theory. Unlike many other books on knot theory, this book has practically no prerequisites; it requires only basic plane and spatial Euclidean geometry but no knowledge of topology or group theory. It contains the first elementary proof of the existence of the Alexander polynomial of a knot or a link based on the Conway axioms, particularly the Conway skein relation. The book also contains an elementary exposition of the Jones polynomial, HOMFLY polynomial and Vassiliev knot invariants constructed using the Kontsevich integral. Additionally, there is a lecture introducing the braid group and shows its connection with knots and links.
Other important features of the book are the large number of original illustrations, numerous exercises and the absence of any references in the first eleven lectures. The last two lectures differ from the first eleven: they comprise a sketch of non-elementary topics and a brief history of the subject, including many references.
Contents
Knots and links, Reidmeister moves
The Conway polynomial
The arithemtic of knots
Some simple knot invariants
The Kauffman bracket
The Jones polynomial
Braids
Discriminants and finite type invariants
Vassiliev invariants
Combinatorial description of Vassiliev invariants
The Kontsevich integrals
Other important topics
A brief history of knot theory
Bibliography
Index
