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...

A canonically defined mod 2 linear dependency current is associated to each collection ν of sections, ν 1 , ..., ν m , of a real rank n vector bundle. This current is supported on the linear dependency set of ν. It is defined whenever the collection ν satisfies a weak measure theoretic condition called " atomicity ". Essentially any reasonable collection of sections satisfies this condition, va...

This paper is a synthesis and extension of three earlier papers on $PD_4$-complexes $X$ with fundamental group $\pi$ such that $c.d.\pi=2$ has one end. Our goal to show the homotopy types complexes are determined by $\pi$, Stiefel-Whitney classes equivariant intersection pairing $\pi_2(X)$. We achieve this under further conditions $\pi$.