A functorial approach to the one-variable Jones Polynomial

R.J. Lawrence

Abstract: 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.

Keywords: Jones polynomial, monodromy representations, braid group, Hecke algebra, Burau representation.

AMS subject classification: 57M25 20F36

Length: 22 pages

Reference: J. Diff. Geom. 37 (1993) 689-710 MR1217166 (95f:57013) (review by Xiao-Song Lin .)

Last updated on September 4th, 1996.