On R-matrix approaches to knot invariants

Abstract

We present an elementary introduction to one of the most important today knot theory approaches, which gives rise to a representation for a class of knot polynomials in terms of quantum groups. Historically, the approach was at the same time developed from the state model approach and from the braid group approach, and we consider the both approaches and there relation to each other and to the R-matrix approach in details with help of the simple explicit examples. We also discuss various kind of motivation for referring to the above approaches as to the physical approaches in knot theory. For instance, we concern a highly inspiring QFT interpretation for a knot polynomial.