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

Nathan Geer; Bertrand Patureau-Mirand

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arXiv · math/0601291

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

Nathan Geer·Bertrand Patureau-Mirand

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Abstract

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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Nathan Geer, Bertrand Patureau-Mirand. 2006-10-19. Multivariable link invariants arising from sl(2|1) and the Alexander polynomial. https://arxiv.org/abs/math/0601291

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