The Springer variety is the set of flags stabilized by a nilpotent operator. In 1976, T.A. Springer observed that this variety’s cohomology ring carries a symmetric group action, and he offered a deep geometric construction of this action. Sixteen years later, Garsia and Procesi made Springer’s work more transparent and accessible by presenting the cohomology ring as a graded quotient of a poly...

Chen and Ruan [6] defined a very interesting cohomology theoryChen-Ruan orbifold cohomology. The primary objective of this paper is to compute the Chen-Ruan orbifold cohomology of the weighted projective spaces, one of the most important space used in physics. The classical tools (orbifold cohomology defined by Chen and Ruan, toric varieties, the localization technique) which have been proved t...

This paper is a part of a larger project devoted to the study of Floer cohomology in algebro-geometic context, as a natural cohomology theory defined on a certain class of ind-schemes. Among these ind-schemes are algebro-geometric models of the spaces of free loops. Let X be a complex projective variety. Heuristically, HQ(X), the quantum cohomology of X, is a version of the Floer cohomology of ...

We propose a method for computing the Z2–cohomology ring of a simplicial complex uniquely associated with a three–dimensional digital binary–valued picture I. Binary digital pictures are represented on the standard grid Z, in which all grid points have integer coordinates. Considering a particular 14–neighbourhood system on this grid, we construct a unique simplicial complex K(I) topologically ...

Let G be a finite group, and R be a commutative ring. This note proposes a generalization to any Green functor for G over R of the construction of the Hochschild cohomology ring HH∗(G,R) from the ordinary cohomology functor H∗(−, R). Another special case is the construction of the crossed Burnside ring of G from the ordinary Burnside functor. The general abstract setting is the following : let ...

In this paper we study the Hochschild cohomology ring of convolution algebras associated to orbifolds, as well as their deformation quantizations. In the first case the ring structure is given in terms of a wedge product on twisted polyvectorfields on the inertia orbifold. After deformation quantization, the ring structure defines a product on the cohomology of the inertia orbifold. We study th...

For GKM manifolds the equivariant cohomology ring of the manifold is isomorphic to the cohomology ring of its GKM graph. In this paper we explore the implications of this fact for equivariant fibrations for which the total space and the base space are both GKM and derive a graph theoretical version of the Serre-Leray theorem. We also make some applications of this result to the equivariant coho...

We construct a dGBV algebra from Dolbeault complex of any closed hyperkk ahler manifold. A Frobenius manifold structure on an neighborhood of the origin in Dolbeault cohomology then arises via Manin's generalization of Barannikov-Kontsevich's construction of formal Frobenius manifold structure on formal extended moduli space of a Calabi-Yau manifold. It is explained why these two kinds of forma...

We introduce the inertial cohomology ring NH T (Y) of a stably almost complex manifold carrying an action of a torus T . We show that in the case that Y has a locally free action by T , the inertial cohomology ring is isomorphic to the Chen-Ruan orbifold cohomology ring H∗CR(Y/T ) (as defined in [Chen-Ruan]) of the quotient orbifold Y/T . For Y a compact Hamiltonian T -space, we extend to orbif...

Let X be a rational homogeneous space and let QH(X)× loc be the group of invertible elements in the small quantum cohomology ring of X localised in the quantum parameters. We generalise results of [ChMaPe06] and realise explicitly the map π1(Aut(X)) → QH (X)× loc described in [Se97]. We even prove that this map is an embedding and realise it in the equivariant quantum cohomology ring QH T (X)× ...