We describe the integral cohomology rings of the flag manifolds of types Bₙ, Dₙ, G₂ and F₄ in terms of their Schubert classes. The main tool is the divided difference operators of Bernstein-Gelfand-Gelfand and Demazure. As an application, we compute the Chow rings of the corresponding complex algebraic groups, recovering thereby the results of R. Marlin.
We use known results on the characteristic rank of the canonical –plane bundle over the oriented Grassmann manifold to compute the generators of the –cohomology groups for . Drawing from the similarities of these examples with the general description of the cohomology rings of we conjecture some predictions.
We estimate the characteristic rank of the canonical –plane bundle over the oriented Grassmann manifold . We then use it to compute uniform upper bounds for the –cup-length of for belonging to certain intervals.
DI(4) is the only known example of an exotic 2-compact group, and is conjectured to be the only one. In this work, we study generalized cohomology theories for DI(4) and its classifying space. Specifically, we compute the Morava K-theories, and the P(n)-cohomology of DI(4). We use the non-commutativity of the spectrum P(n) at p=2 to prove the non-homotopy nilpotency of DI(4). Concerning the classifying space, we prove that the BP-cohomology and the Morava K-theories of BDI(4) are all concentrated...
Cette note évoque les premiers travaux de J.-L. Koszul (1947-1950) en les replaçant dans leur cadre historique et retrace en particulier le chemin qui a conduit Koszul à la résolution qui porte son nom.
In this paper, we consider several invariant complex structures on a compact real nilmanifold, and we study relations between invariant complex structures and Hodge numbers.