The Hochschild cohomology of a closed manifold

Second Hochschild Cohomology of Convolution Algebras

The Hochschild Cohomology of a Poincaré Algebra

In this note, we define the notion of a cactus set, and show that its geometric realization has a natural structure as an algebra over Voronov’s cactus operad, which is equivalent to the framed 2-dimensional little disks operad D2. Using this, we show that for a Poincaré algebra A, its Hochschild cohomology is an algebra over the (chain complexes of) D2.

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...

Alternated Hochschild Cohomology

In this paper we construct a graded Lie algebra on the space of cochains on a Z2-graded vector space that are skew-symmetric in the odd variables. The Lie bracket is obtained from the classical Gerstenhaber bracket by (partial) skew-symmetrization; the coboundary operator is a skew-symmetrized version of the Hochschild differential. We show that an order-one element m satisfying the zero-square...

Hochschild Cohomology of Truncated Polynomials

The main result of this paper is to calculate the Batalin-Vilkovisky structure of HH∗(C∗(KPn;R);C∗(KPn;R)) for K = C andH, and R = Z and any field; and shows that in the special case when M = CP 1 = S2, and R = Z, this structure can not be identified with the BV-structure of H∗(LS 2;Z) computed by Luc Memichi in [16]. However, the induced Gerstenhaber structures are still identified in this cas...