Multivariable link invariants arising from sl(2|1) and the Alexander polynomial

Details Multivariable link invariants arising from sl(2|1) and the Alexander polynomial Multivariable link invariants arising from sl(2|1) and the Alexander polynomial

2006-01-12

arxiv.org/abs/math/0601291v2

Mathematics

Geometric Topology

19 pages, to appear in Journal of Pure and Applied Algebra. Several changes and a proof added. (see math.GT/0609034 for other

Scientific paper

In this paper we construct a multivariable link invariant arising from the quantum group associated to the special linear Lie superalgebra sl(2|1). The usual quantum group invariant of links associated to (generic) representations of sl(2|1) is trivial. However, we modify this construction and define a nontrivial link invariant. This new invariant can be thought of as a multivariable version of the Links-Gould invariant. We also show that after a variable reduction our invariant specializes to the Conway potential function, which is a version of the multivariable Alexander polynomial.

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