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

m at h . A T ] 2 6 M ay 2 00 5 Chromatic numbers , morphism complexes , and Stiefel - Whitney characteristic classes . Dmitry N . Kozlov

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...

V Turaev, Poincaré-Reidemeister metric, Euler structures, and torsion

In this paper we define a Poincaré-Reidemeister scalar product on the determinant line of the cohomology of any flat vector bundle over a closed orientable odd-dimensional manifold. It is a combinatorial “torsion-type” invariant which refines the PR-metric introduced in [Fa] and contains an additional sign or phase information. We compute the PR-scalar product in terms of the torsions of Euler ...

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.

Multiple point of self-transverse immesions of certain manifolds

In this paper we will determine the multiple point manifolds of certain self-transverse immersions in Euclidean spaces. Following the triple points, these immersions have a double point self-intersection set which is the image of an immersion of a smooth 5-dimensional manifold, cobordant to Dold manifold $V^5$ or a boundary. We will show there is an immersion of $S^7times P^2$ in $mathbb{R}^{1...