Newstead gave the generators of cohomology ring moduli space rank 2 semi-stable, torsion-free sheaves with fixed odd degree determinant over a smooth, projective curve. In this article, we generalize result to case when underlying curve is irreducible, nodal. We show that these (of in nodal case) arise naturally as degeneration Newstead's smooth case.

Suppose that G = S acts freely on a finitistic space X whose mod p cohomology ring isomorphic to that of a lens space L(p; q1, . . . , qm). In this paper, we determine the mod p cohomology ring of the orbit space X/G. If the characteristic class α ǫH(X/G;Zp) of the S -bundle S →֒ X → X/G is nonzero, then the mod p index of the action is defined to be the largest integer n such that α 6= 0. We al...

We identify the ring of odd symmetric functions introduced by Ellis and Khovanov as the space of skew polynomials fixed by a natural action of the Hecke algebra at q = −1. This allows us to define graded modules over the Hecke algebra at q = −1 that are ‘odd’ analogs of the cohomology of type A Springer varieties. The graded module associated to the full flag variety corresponds to the quotient...

The aim of this article is to give a concise algebraic treatment of the modular symbols formalism, generalised from modular curves to Hecke triangle surfaces. A sketch is included of how the modular symbols formalism gives rise to the standard algorithms for the computation of holomorphic modular forms. Precise and explicit connections are established to the cohomology of Hecke triangle surface...

We establish the formula for multiplication by the class of a special Schubert variety in the integral cohomology ring of the flag manifold. This formula also describes the multiplication of a Schubert polynomial by either an elementary symmetric polynomial or a complete homogeneous symmetric polynomial. Thus, we generalize the classical Pieri’s rule for symmetric polynomials/Grassmann varietie...

Let G be a finite group, F an algebraically closed field of finite characteristic p, and let B be a block of FG. We show that the Hochschild and Linckelmann cohomology rings of B are isomorphic, modulo their radicals, in the cases where (1) B is cyclic and (2) B is arbitrary and G either a nilpotent group or a Frobenius group (p odd). (The second case is a consequence of a more general result)....

We also give partial results on computation of cohomology groups on U for a locally constant sheaf of general rank and on computation of H(C \ Z,C) where Z is a general algebraic set. Our algorithm is based on computations of Gröbner bases in the ring of differential operators with polynomial coefficients, algorithms for functors in the theory of D-modules ([24] and [25]), and Grothendieck-Deli...

This leads to two ways to construct the ring cohomology: cohomology for rings which are regarded as algebras due to Shukla [Sh], and ring cohomology due to Mac Lane [Mac]. The ring structure has been categorized by the definition of an Ann-category [4]. Each congruence class of Ann-categories is characterized by a cohomology class of structures (Theorem 4.3[4]). For regular Ann-categories, this...

Let C be a small category and k a field. There are two interesting mathematical subjects: the category algebra kC and the classifying space |C| = BC. We study the ring homomorphism HH∗(kC) → H∗(|C|, k) and prove it is split surjective, using the factorization category of Quillen [16] and certain techniques from functor cohomology theory. This generalizes the well-known results for finite groups...

Homotopy groups of a connective ring spectrum R form an Ngraded algebra π∗R which is commutative if R is commutative. We describe a secondary algebra π∗,∗R which enriches the structure of the algebra π∗R in a new unexpected way. The algebra π∗,∗R encodes secondary homotopy operations in π∗R, such as Toda brackets, and the first Postnikov invariant of R as a ring spectrum. Moreover, π∗,∗R repres...