A Hennings type invariant of 3-manifolds from a topological Hopf superalgebra

Abstract

We prove the unrolled superalgebra ${\mathcal{U}}_{\xi }^H\mathfrak{sl}(2|1)$ has a completion which is a ribbon Hopf superalgebra in a topological sense where $\xi$ is a root of unity of odd order. Using this ribbon Hopf superalgebra we construct its universal invariant of links. We use it to construct an invariant of 3-manifolds endowed with a first cohomology class of Hennings type.