ABSTRACT
This chapter shows how different branches of low-dimensional topology can interact and provides very strong results. It describes a sympathetic theory of knots. The chapter describes some fundamental constructions of three-dimensional topology, such as the Heegaard decomposition, and the Kirby moves. They are necessary for constructing the Witten theory; they have their own remarkable interest. The theory of Witten-Reshetikhin-Turaev invariants, which is based on the Kauffman bracket on one hand and the Kirby theory on the other, is very deep. The Fenn-Rourke theorem states that in order to establish that two three manifolds given by planar diagrams of framed links are diffeomorphic; it is necessary and sufficient to construct a chain of R. Fenn-C. Rourke moves transforming one diagram to the other one.
