Stiefel-Whitney Homology Classes and Singularities of Projections for Polyhedral Manifolds
by Thomas F. Banchoff

Stiefel-Whitney classes of simplicial manifolds can be defined in terms of projections into Euclidean spaces. This paper presents an explicit chain associated with a projection. This is used to formulate a homology class that is independent of the projection, and it is shown that this class is dual to a Stiefel-Whitney cohomology class of the manifold.