Basic intersection cohomology of conical fibrations

We introduce notions of singular fibration and singular Seifert fibration. These notions naturally generalize that o locally trivial fibration to the category of stratified pseudomanifolds. For singular foliations determined by such fibrations, we prove the de Rham theorem for basic intersection cohomology recently introduced by the present authors. One of the main examples of such a structure is the natural projection to the space of fibers of a singular Riemannian foliation determined by a Lie group action on a compact smooth manifold.