Introduction to Knot Theory

Traditionally, knot theory deals with diagrams of knots and the search of invariants of diagrams which are invariant under the well known Reidemeister moves. This book goes one step beyond: it gives a method to construct invariants for one parameter families of diagrams and which are invariant under higher Reidemeister moves.

Knots in 3-Space and the Solid Torus

Luckily, knots in 3-space, often called classical knots, can be transformed into knots in the solid torus without loss of information. It turns out that knots in the solid torus have a particular rich topological moduli space.

It contains many canonical loops to which the invariants for one parameter families can be applied, in order to get a new sort of invariants for classical knots.