The Links-Gould Invariant of Links

Details The Links-Gould Invariant of Links The Links-Gould Invariant of Links

1998-11-23

arxiv.org/abs/math/9811128v2

Journal of Knot Theory and its Ramifications, 8(2):165-199, March 1999

Mathematics

Geometric Topology

35 pages, 20 figures. <ddw@maths.uq.edu.au>, <kauffman@uic.edu>, <http://math.uic.edu/~kauffman>, <jrl@maths.uq.edu.au>

Scientific paper

We introduce and study in detail an invariant of (1,1) tangles. This invariant, derived from a family of four dimensional representations of the quantum superalgebra U_q[gl(2|1)], will be referred to as the Links-Gould invariant. We find that our invariant is distinct from the Jones, HOMFLY and Kauffman polynomials (detecting chirality of some links where these invariants fail), and that it does not distinguish mutants or inverses. The method of evaluation is based on an abstract tensor state model for the invariant that is quite useful for computation as well as theoretical exploration.

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