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

2006/01/12 by Geer, Nathan, Patureau-Mirand, Bertrand · 3 citations
#17B37 #57M25 #57M27 #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.math/0601291

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.

Cited by

• On the colored Links--Gould polynomial
• Quantum invariants of 3-manifolds and links: a review
• A supergroup series for knot complements

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