A functorial approach to the one-variable jones polynomial

In this paper, a representation of the category of tangles will be given, which has a natural meaning in terms of certain twisted homology groups. The representation is demonstrated explicitly in terms of a presentation of this category found by Turaev. The invariant of links obtained is identified with the one-variable Jones polynomial via the skein relation, and some remarks are made on how the procedure can be extended to give the two-variable Jones polynomial.