ORBIFOLD CUP PRODUCTS AND RING STRUCTURES ON HOCHSCHILD COHOMOLOGIES

Orbifold Cup Products and Ring Structures on Hochschild Cohomologies

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...

Netherlands Cup products and mixed Hodge structures

Let X be a complete complex algebraic variety of dimension n and let D be a divisor with strict normal crossings on X. In this paper we show that the cup product maps i+j D (X) are morphisms of mixed Hodge structures.

Note on Cup-products

On algebraic structures of the Hochschild complex

We first review various known algebraic structures on the Hochschild (co)homology of a differential graded algebras under weak Poincaré duality hypothesis, such as CalabiYau algebras, derived Poincaré duality algebras and closed Frobenius algebras. This includes a BV-algebra structure on HH(A,A) or HH(A,A), which in the latter case is an extension of the natural Gerstenhaber structure on HH(A,A...

Finite Groups Acting Linearly: Hochschild Cohomology and the Cup Product

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...