Topological invariants from quantum group ${\mathcal{U}}_{\xi }\mathfrak{s}\mathfrak{l}(2\mathrm{\mid }1)$ at roots of unity

In this article we construct link invariants and 3-manifold invariants from the quantum group associated with Lie superalgebra $\mathfrak{s}\mathfrak{l}(2\mathrm{\mid }1)$. This construction based on nilpotent irreducible finite dimensional representations of quantum group ${\mathcal{U}}_{\xi }\mathfrak{s}\mathfrak{l}(2\mathrm{\mid }1)$ where $\xi$ is a root of unity of odd order. These constructions use the notion of modified trace and relative $G$-modular category.