KNOTS, SATELLITES AND QUANTUM GROUPS

The following sections are included:

• Introduction

  • Setting the scene

  • Background

  • Knot diagrams and moves

  • Links and linking number

  • Framed links

  • Satellites

• Homfly invariants

• General Homfly skein theory

  • Composition

  • Closure

• The skein of the annulus

  • Meridian maps

  • Partitions

  • Branching rules in C

• Symmetric functions and the skein of the annulus

  • Symmetric functions

  • Construction of the basis elements

• Unitary quantum invariants

  • Basic constructions of quantum invariants

• Manifold invariants

  • Surgery presentation

  • Manifolds with boundary

  • Evaluation of knot invariants

  • Level invariants for manifolds

• References