Different links with the same Links-Gould invariant

Abstract

Using the skein relations for the Links-Gould (LG) invariant discovered by the first author, we give two constructions to provide a pair of different knots or links sharing the same LG invariant. Using this, we give examples of arbitrarily many 2-bridge knots with the same LG invariant. These knots also share the same HOMFLY and Kauffman polynomials. Further, for 2-bridge links we construct a similar example, which also share the same 2-variable Alexander polynomial. We also give a non-amphicheiral hyperbolic knot whose chirality is not undetected by the LG invariant.