The problem of gauging a closed form is considered. When the target manifold is a simple Lie group G, it is seen that there is no obstruction to the gauging of a subgroup H ⊂ G if we may construct from the form a cocycle for the relative Lie algebra cohomology (or for the equivariant cohomology), and a general expression for these cocycles is given. Their formal similarity with the expressions ...

For each group G having an infinite normal subgroup with the relative property (T) (for instance groups of the form G = H ×K, where H is infinite with property (T) and K is arbitrary) and each countable abelian group Λ we construct free ergodic measure-preserving actions σΛ on the probability space such that the 1’st cohomology group of σΛ, H (σΛ), is equal to Char(G)×Λ. We deduce that G has un...

In this paper the authors investigate infinite-dimensional representations L in blocks of the relative (parabolic) category OS for a complex simple Lie algebra, having the property that the cohomology of the nilradical with coefficients in L “looks like” the cohomology with coefficients in a finite-dimensional module, as in Kostant’s theorem. A complete classification of these “Kostant modules”...

Let p be a fixed prime number, V a group isomorphic to (Z/p) for some integer d and BV its classifying space. The exceptional properties of the mod p cohomology of BV , as an unstable module and algebra over the Steenrod algebra, have led to the calculation of the mod p cohomology of the mapping spaces with source BV as the image by a functor TV of the mod p cohomology of the target ([La2]). Th...

let $a$ be an abelian topological group and $b$ a trivial topological $a$-module. in this paper we define the second bilinear cohomology with a trivial coefficient. we show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...

For a smooth scheme X of pure dimension d over field k and an effective Cartier divisor D⊂X whose support is simple normal crossing divisor, we construct cycle class map from the Chow group zero-cycles with modulus to cohomology relative Milnor K-sheaf.

For a smooth scheme X of pure dimension d over field k and an effective Cartier divisor D⊂X whose support is simple normal crossing divisor, we construct cycle class map from the Chow group zero-cycles with modulus to cohomology relative Milnor K-sheaf.