The ADO invariants are a sequence of non-semisimple quantum invariants coming from the representation theory of the quantum group U_q(sl(2)) at roots of unity. Ito showed that these invariants are sums of traces of quotients of homological representations of braid groups (truncated Lawrence representations). In this paper we show a direct homological formula for the ADO invariants, as sums of partial traces of Lawrence type representations, without further truncations.

This paper was prepared at the University of Oxford, and I acknowledge the support of the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 674978). I am grateful to the anonymous referee for useful comments and suggestions about an earlier version of this paper.