Stiefel-whitney Classes for Representations of Groups

Stiefel-whitney Classes for Coherent Real Analytic Sheaves

We develop Stiefel-Whitney classes for coherent real analytic sheaves and investigate their applications to analytic cycles on real analytic manifolds.

Characteristic Classes and Quadric Bundles

In this paper we construct Stiefel-Whitney and Euler classes in Chow cohomology for algebraic vector bundles with nondegenerate quadratic form. These classes are not in the algebra generated by the Chern classes of such bundles and are new characteristic classes in algebraic geometry. On complex varieties, they correspond to classes with the same name pulled back from the cohomology of the clas...

On Representations and K-theory of the Braid Groups

Let Γ be the fundamental group of the complement of a K(Γ, 1) hyperplane arrangement (such as Artin’s pure braid group) or more generally a homologically toroidal group as defined below. The subgroup of elements in the complex K-theory of BΓ which arises from complex unitary representations of Γ is shown to be trivial. In the case of real K-theory, this subgroup is an elementary abelian 2-group...

On the Stiefel-whitney Classes of a Manifold. Ii

Chromatic Numbers, Morphism Complexes, and Stiefel-whitney Characteristic Classes