We introduce crossed interval groups and construct a crossed interval analog IS of the Fiedorowicz-Loday symmetric category ∆S. We prove that the functor FS(−) of the free IS-extension of an I-object does not change homotopy type. We then observe that the operad B of natural operations on the Hochschild cohomology equals FS(T ), where T is an operad whose homotopy type is known. We conclude fro...

Let G be an exceptional Lie group with a maximal torus T , and let Ap be the mod–p Steenrod algebra. Based on common properties in the Schubert presentation of the cohomology H∗(G/T ; Fp), we obtain a complete characterization for the Ap–algebra H ∗(G; Fp). 2000 Mathematical Subject Classification: 57T15; 14M15. Email addresses: [email protected]; [email protected]

The Riemann–Roch theorem for multiplicative operations in oriented cohomology theories for algebraic varieties is proved and an explicit formula for the corresponding Todd classes is given. The formula obtained can also be applied in the topological situation, and the theorem can be regarded as a change-of-variables formula for the integration of cohomology classes. The classical Riemann–Roch t...

We describe a variant construction of the unstable Adams spectral sequence for space $Y$, associated to any free simplicial resolution $H^*(Y;R)$ $R=\mathbb{F}_p$ or $\mathbb{Q}$. use this differentials and filtration in terms appropriate systems higher cohomology operations.

The aim of this paper is to compute a simplicial cohomology group of some specific digital images. Then we define ringand algebra structures of a digital cohomology with the cup product. Finally, we prove a special case of the Borsuk-Ulam theorem fordigital images.

This paper is concerned with the relation between local cohomology modules defined by a pair of ideals and the Serre subcategories of the category of modules. We characterize the membership of local cohomology modules in a certain Serre subcategory from lower range or upper range.

certain algebraic invariants of the integral group ring zg of a group g were introduced and investigated in relation to the problem of extending the farrell-tate cohomology, which is defined for the class of groups of finite virtual cohomological dimension. it turns out that the finiteness of these invariants of a group g implies the existence of a generalized farrell-tate cohomology for g whic...

Abstract In 1947, N.E. Steenrod defined the Squares, which are mod 2 cohomology operations, using explicit cochain formulae for cup- i products of cocycles. He later recast construction in more general homological terms, group homology and acyclic model methods, rather than formulae, to define p operations all primes . Steenrod’s student J. Adem applied point view prove fundamental relations, k...