The computation and understanding of quantum cohomology is a very hard problem in mathematical physics (string theory). We review in non-technical terms how in case of the ag manifolds this problem turns out to be at its core a non-trivial problem in algebraic combinatorics. The basic quest of physics in the 20th century is that for a uniied theory of the physical world. During the 80's string ...

Quandle cohomology theory was developed [5] to define invariants of classical knots and knotted surfaces in state-sum form, called quandle cocycle (knot) invariants. The quandle cohomology theory is a modification of rack cohomology theory which was defined in [11]. The cocycle knot invariants are analogous in their definitions to the Dijkgraaf-Witten invariants [8] of triangulated 3-manifolds ...

We introduce a generalization of formal local cohomology module, which we call a formal local cohomology module with respect to a pair of ideals and study its various properties. We analyze their structure, the upper and lower vanishing and non-vanishing. There are various exact sequences concerning the formal cohomology modules. Among them a MayerVietoris sequence for two ideals with respect t...

An important combinatorial result in equivariant cohomology and K-theory Schubert calculus is represented by the formulas of Billey and Graham-Willems for the localization of Schubert classes at torus fixed points. These formulas work uniformly in all Lie types, and are based on the concept of a root polynomial. In this paper we define formal root polynomials associated with an arbitrary formal...

The analogue of Lagrangians for symplectic forms over finite groups is studied, motivated by the fact that symplectic G-forms with a normal Lagrangian N⊳G are in one-to-one correspondence, up to inflation, with bijective 1-cocycle data on the quotients G/N . This yields a method to construct groups of central type from such quotients, known as Involutive Yang-Baxter groups. Another motivation f...

Introduction. Let G be a group, K an invariant subgroup of G. The purpose of this paper is to investigate the relations between the cohomology groups of G, K, and G/K. As in the case of fibre spaces, it turns out that such relations can be expressed by a spectral sequence whose term E2 is HiG/K, HiK)) and whose term Em is the graduated group associated with i7(G). This problem was first studied...