We study the Poisson (co)homology of the algebra of truncated polynomials in two variables viewed as the semi-classical limit of a quantum complete intersection studied by Bergh and Erdmann. We show in particular that the Poisson cohomology ring of such a Poisson algebra is isomorphic to the Hochschild cohomology ring of the corresponding quantum complete intersection.

Moduli spaces arise in classification problems in algebraic geometry (and other areas of geometry) when, as is typically the case, there are not enough discrete invariants to classify objects up to isomorphism. In the case of nonsingular complex projective curves (or compact Riemann surfaces) the genus g is a discrete invariant which classifies the curve regarded as a topological surface, but d...

In the fifties, Saunders Mac Lane invented a cohomology theory of rings using the cubical construction introduced earlier by Eilenberg and himself to calculate stable homology of Eilenberg-Mac Lane spaces. As shown in [9], this theory coincides with the topological Hochschild cohomology for Eilenberg-Mac Lane ring spectra. In particular, the third dimensional cohomology group is expected to pro...

Let X be a finitistic space with non-trivial cohomology groups H (X;Z) ∼= Z with generators vi , where i = 0, 1, 2, 3. We say that X has cohomology type (a, b) if v 1 = av2 and v1v2 = bv3 . In this note, we determine the mod 2 cohomology ring of the orbit space X/G of a free action of G = Z2 on X , where both a and b are even. In this case, we observed that there is no equivariant map S → X for...

In this short note, we study the semi-simplicity of the quantum cohomology algebras of smooth Fano complete intersections in projective space. Let V be a smooth Fano manifold with a symplectic form ω. The quantum cohomology on V is the cohomology H(V,Z{H2(V )}) with a ring structure defined by the GW-invariants. The Novikov ring Z{H2(V )} can be described as follows: choose a basis q1, · · · , ...

We study an integration theory in circle equivariant cohomology in order to prove a theorem relating the cohomology ring of a hyperkähler quotient to the cohomology ring of the quotient by a maximal abelian subgroup, analogous to a theorem of Martin for symplectic quotients. We discuss applications of this theorem to quiver varieties, and compute as an example the ordinary and equivariant cohom...

Cohomology groups and the cohomology ring of threedimensional (3D) objects are topological invariants that characterize holes and their relations. Cohomology ring has been traditionally computed on simplicial complexes. Nevertheless, cubical complexes deal directly with the voxels in 3D images, no additional triangulation is necessary. This could facilitate efficient algorithms for the computat...

When a finite group acts linearly on a complex vector space, the natural semi-direct product of the group and the polynomial ring over the space forms a skew group algebra. This algebra plays the role of the coordinate ring of the resulting orbifold and serves as a substitute for the ring of invariant polynomials from the viewpoint of geometry and physics. Its Hochschild cohomology predicts var...

We show that the equivariant Chow cohomology ring of a toric variety is naturally isomorphic to the ring of integral piecewise polynomial functions on the associated fan. This gives a large class of singular spaces for which localization holds in equivariant Chow cohomology with integer coefficients. We also compute the equivariant Chow cohomology of toric prevarieties and general complex hyper...