A remark on Hochschild cohomology and Koszul duality

A Remark on Koszul Complexes

j j mj m b mj mi for all m mi M When M is a nite free R module then the vanishing of the homology of K is determined by the grade g of the ideal Im one hasHj K for j n g n and Hn g K Giving a linear form on a nite free R module of rank n is equivalent to specifying a sequence a an of elements of R If M is not a free R module then the picture changes drastically In this note we investigate the s...

Equivariant cohomology, Koszul duality, and the localization theorem

(1.1) This paper concerns three aspects of the action of a compact group K on a space X . The ®rst is concrete and the others are rather abstract. (1) Equivariantly formal spaces. These have the property that their cohomology may be computed from the structure of the zero and one dimensional orbits of the action of a maximal torus in K. (2) Koszul duality. This enables one to translate facts ab...

Gale Duality and Koszul Duality

Given a hyperplane arrangement in an affine space equipped with a linear functional, we define two finite-dimensional, noncommutative algebras, both of which are motivated by the geometry of hypertoric varieties. We show that these algebras are Koszul dual to each other, and that the roles of the two algebras are reversed by Gale duality. We also study the centers and representation categories ...

On Kontsevich’s Hochschild cohomology conjecture

Higher order Hochschild cohomology

Following ideas of Pirashvili, we define higher order Hochschild cohomology over spheres S defined for any commutative algebra A and module M . When M = A, we prove that this cohomology is equipped with graded commutative algebra and degree d Lie algebra structures as well as with Adams operations. All operations are compatible in a suitable sense. These structures are related to Brane topology...