Invariants homològics de nusos

Abstract

This essay encompasses, first, some basic concepts related to knot theory. Secondly, we will deal with knot polynomials, presenting how the definition of the Jones polynomial can be reached by means of the Kauffman bracket. In the third chapter we will define co)homology of (co)chain complexes for its use in the fourth chapter. The main objective of this work is to learn how to compute Khovanov homology, which we deal with in the fourth chapter, where some Khovanov homology computations will also be carried out, with the purpose of extracting valuable conclusions therefrom. Finally, in the concluding section, we will present a global view of knot theory nowadays.