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.
Original language | American English |
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Pages (from-to) | 689-710 |
Number of pages | 22 |
Journal | Journal of Differential Geometry |
Volume | 37 |
Issue number | 3 |
DOIs | |
State | Published - May 1993 |
Externally published | Yes |