The main result of this paper is a computation of the motivic cohomology of varieties of n × m-matrices of of rank m, including both the ring structure and the action of the reduced power operations. The argument proceeds by a comparison of the general linear group-scheme with a Tate suspension of a space which is A1-equivalent to projective n− 1-space with a disjoint basepoint.

The category of graded, bicommutative Hopf algebras over the prime eld with p elements is an abelian category which is equivalent, by work of Schoeller, to a category of graded modules, known as Dieudonn e modules. Graded ring objects in Hopf algebras are called Hopf rings, and they arise in the study of unstable cohomology operations for extraordinary cohomology theories. The central point of ...

IN HIS WORK on complex cobordism [ 181 Novikov introduced a spectral sequence converging to the stable homotopy of a space, depending only on the complex cobordism of the space as a module over the ring of primary complex cobordism operations. This spectral sequence can be localized at a prime p and one can work, as Novikov did, with the smaller theory, BP*( ), known as Brown-Peterson cohomolog...

The purpose of this paper is to explain and to generalize, in a homotopical way, the result of Barannikov–Kontsevich and Manin, which states that the underlying homology groups of some Batalin–Vilkovisky algebras carry a Frobenius manifold structure. To this extent, we first make the minimal model for the operad encoding BV-algebras explicit. Then, we prove a homotopy transfer theorem for the a...

The classical Schubert cells on a flag manifold G/H give a cell decomposition for G/H whose Kronecker duals (known as Schubert classes) form an additive base for the integral cohomology H(G/H). We present a formula that expresses Steenrod mod–p operations on Schubert classes in G/H in terms of Cartan numbers of G. 2000 Mathematical Subject Classification: 55S10 (14M10, 1415).

My current and planned research divides into three areas: the relationship between stable and unstable cohomology operations, the differential topology of loop spaces, and the use of category theory in geometry. This research lies in the areas of algebraic topology, differential topology, and differential geometry and it has further application to mathematical physics. In addition to the techni...

This paper offers an algorithmic solution to the problem of obtaining “economical” formulae for some maps in Simplicial Topology, having, in principle, a high computational cost in their evaluation. In particular, maps of this kind are used for defining cohomology operations at the cochain level. As an example, we obtain an explicit combinatorial description of all Steenrod kth powers exclusive...