A Morse-Bott type complex and the Bismut–Zhang torsion for intersection cohomology

In the first part of this article we establish, for a compact pseudomanifold and a given perversity in the sense of Goresky and MacPherson a Morse theoretical cochain complex, which computes the intersection cohomology of the space. In the second part we use this cochain complex as well as the model Witten Laplacian to define the Bismut–Zhang torsion of a pseudomanifold. Conjecturally the Bismut–Zhang torsion will serve as the "topological" side in a Cheeger–Müller theorem for spaces with iterated conical singularities.