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In this article we construct link invariants and 3-manifold invariants fromthe quantum group associated with Lie superalgebra $\mathfrak{sl}(2|1)$. Thisconstruction based on nilpotent irreducible finite dimensional representationsof quantum group $\mathcal{U}_{\xi}\mathfrak{sl}(2|1)$ where $\xi$ is a root ofunity of odd order. These constructions use the notion of modified trace andrelative $\mathit{G}$-modular category.

Topological invariants from quantum group $\mathcal{U}_{\xi}\mathfrak{sl}(2|1)$ at roots of unity