TY - JOUR
T1 - A functorial approach to the one-variable jones polynomial
AU - Lawrence, R. J.
PY - 1993/5
Y1 - 1993/5
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84972526441&partnerID=8YFLogxK
U2 - 10.4310/jdg/1214453905
DO - 10.4310/jdg/1214453905
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AN - SCOPUS:84972526441
SN - 0022-040X
VL - 37
SP - 689
EP - 710
JO - Journal of Differential Geometry
JF - Journal of Differential Geometry
IS - 3
ER -