This work is a contribution to study residues of real characteristic classes of vector bundles on which act compact Lie groups. By using the Cech-De Rham complex, the realisation of the usual Thom isomorphism permites us to illustrate localisation techniques of some topological invariants.
Let be a set of all possible nonequivalent systems of local integer coefficients over the classifying space . We introduce a cohomology ring , which has a structure of a -graded ring, and describe it in terms of generators and relations. The cohomology ring with integer coefficients is contained as its subring. This result generalizes both the description of the cohomology with the nontrivial system of local integer coefficients of in [Č] and the description of the cohomology with integer...
We give a survey of the work of Milnor, Friedlander, Mislin, Suslin and other authors on the Friedlander-Milnor conjecture on the homology of Lie groups made discrete and its relation to the algebraic K-theory of fields.
A bipolynomial is a holomorphic mapping of a sphere onto a sphere such that some point on the target sphere has exactly two preimages. The topological invariants of spaces of bipolynomials without multiple roots are connected with characteristic classes of rational functions with two poles and generalized braid groups associated to extended affine Weyl groups of the serie . We prove that the cohomology rings of the spaces of bipolynomials of bidegree stabilize as tends to infinity and that...