We use a variation of Hatcher’s construction to construct, rationally stably, all exotic smooth structures on smooth manifold bundles whose fibers have sufficiently large odd dimension (at least twice the base dimension q plus 3). We show that, rationally stably, such smooth structures are classified by a cohomology class in the total space and the relative higher Igusa-Klein (IK) torsion is eq...

We introduce the concept of strongly r-matrix induced (SRMI) Poisson structure, report on the relation of this property with the stabilizer dimension of the considered quadratic Poisson tensor, and classify the Poisson structures of the Dufour-Haraki classification (DHC) according to their membership of the family of SRMI tensors. One of the main results of our work is a generic cohomological p...