  The second author constructed a topological ribbon Hopf algebra from the
unrolled quantum group associated with the super Lie algebra
$\mathfrak{sl}(2|1)$. We generalize this fact to the context of unrolled
quantum groups and construct the associated topological ribbon Hopf algebras.
Then we use such an algebra, the discrete Fourier transforms, a symmetrized
graded integral and a modified trace to define a modified graded Hennings
invariant. Finally, we use the notion of a modified integral to extend this
invariant to empty manifolds and show that it recovers the CGP-invariant.
