Topological String Theory Methods of Computer-aided Drug Design/Knots, HOMFLY-PT Polynomial, Chern-Simons Theory and Surgery

This chapter covers knot theory and its invariants, including, especially, HOMFLY-PT polynomials. We explain Witten's viewpoint: these polynomials can be interpreted as the vacuum expectation value of Wilson loop operators in Chern-Simons Theory with gauge group and the fundamental representation. This easily leads to the generalization of HOMFLY-PT polynomials to arbitrary gauge groups and representations. We then introduce Guadagnini's amalgamation of Chern-Simons theory and Dehn surgery: this allows the computation of HOMFLY-PT polynomials in an arbitrary -manifold with given surgery presentation. This includes all -manifolds, due to a result by Lickorish and Wallace. Contents Knot theory Link invariants HOMFLY-PT polynomials Chern-Simons Theory Surgery HOMFLY-PT polynomials in arbitrary -manifolds