3 Planar Algebras

Summary.Another approach for understanding knot theory as a finitely presented theory is within the context of planar algebras which we will review is Section 3.1. Within the context of planar algebras, knot theory has a very nice (and familiar) decription -- it is the theory generated by crossings modulo the standard Reidemeister moves. Even the syzygies of this theory are simply enumerated by codimension two singular plane projections. For now, see [BN8,BN9].

- 3.1 A quick introduction to planar algebras
- 3.2 The standard planar algebras of tangles and of chord diagrams and the no-go theorem
- 3.3 Shielded chord diagrams and tangles
- 3.4 Generators, relations and syzygies

Dror Bar-Natan 2001-07-23