The Steenrod p-powers in Whitney cohomology

In his Ph.D. thesis and in the paper Whitney stratified chains and cochains, M. Goresky introduced, associated to each Whitney stratification X, a geometric cohomology theory WH∗(X), showing that there is a bijection Rk : WHk(X) → Hk(X). Subsequently, in 1994 I improved Goreskyʹs theory, by first introducing a group operation in WHk(X), geometrically defined via transverse union of cochains in such a way that the representation map Rk becomes a group isomorphism, and secondly by giving a geometric construction of the Steenrod squares. s paper, extending techniques and results of Murolo (1994), we complete the theory by constructing geometrically (through the transversal sum), the Steenrod p-powers in the context of Whitney cohomology WH∗. A preliminary analysis explaining the Whitney cohomology of the lens spaces Lp = ShZp is necessary.