In the present paper we provide a general algorithm to compute multiplicative cohomological operations on algebraic oriented cohomology of projective homogeneous G-varieties, where G is split reductive group over field k characteristic 0. More precisely, extend such respective T-equivariant (T maximal torus G) theories, and then them using equivariant Schubert calculus techniques. This generali...

We study the Lie module structure given by the Gerstenhaber bracket on the Hochschild cohomology groups of a monomial algebra with radical square zero. The description of such Lie module structure will be given in terms of the combinatorics of the quiver. The Lie module structure will be related to the classification of finite dimensional modules over simple Lie algebras when the quiver is give...

We prove a relationship between quantum Steenrod operations and the connection. In particular there are extending power that, when viewed as endomorphisms of equivariant cohomology, covariantly constant. demonstrate how this property is used in computations examples.

The aim of this work is to describe some operations in the category of regular holonomic D-modules with support a normal crossing and variation zero introduced in [2]. These operations will allow us to compute the characteristic cycle of the local cohomology supported on homogeneous prime ideals of these modules. In particular, we will be able to describe their Bass and dual Bass numbers.

The natural partial ordering of the orbit types of the action of the group of local gauge transformations on the space of connections in space-time dimension d ≤ 4 is investigated. For that purpose, a description of orbit types in terms of cohomology elements of space-time, derived earlier, is used. It is shown that, on the level of these cohomology elements, the partial ordering relation is ch...

We explore several variations of the notion of purity for the action of Frobenius on schemes defined over finite fields. In particular, we study how these notions are preserved under certain natural operations like quotients for principal bundles and also geometric quotients for reductive group actions. We then apply these results to study the cohomology of quiver moduli. We prove that a natura...

We examine some of the basic properties satisfied by Bloch’s cycle complexes for quasi-projective varieties over a field, and extend some of them to the cycle complex of a scheme of finite type over a regular dimension one base. We also give an extension to the simplicial spectra in the niveau tower of the cosimplicial scheme ∆∗ X . As applications, we show that the AtiyahHirzebruch spectral se...

We define a category Fat whose objects are isomorphism classes of bordered fat graphs and show that its geometric realization is a classifying space for the bordered mapping class groups. We then construct a CW structure on this geometric realization with one cell per isomorphism classes of bordered fat graphs. Its cellular cochain complex gives a bordered graph complex which computes the integ...

This paper studies the (small) quantum homology and cohomology of fibrations p : P → S whose structural group is the group of Hamiltonian symplectomorphisms of the fiber (M,ω). It gives a proof that the rational cohomology splits additively as the vector space tensor product H(M)⊗H(S), and investigates conditions under which the ring structure also splits, thus generalizing work of Lalonde–McDu...