We study cohomology theories of strongly homotopy algebras, namely A∞, C∞ and L∞-algebras and establish the Hodge decomposition of Hochschild and cyclic cohomology of C∞-algebras thus generalising previous work by Loday and Gerstenhaber-Schack. These results are then used to show that a C∞-algebra with an invariant inner product on its cohomology can be uniquely extended to a symplectic C∞-alge...

We prove the Cartan–Eilenberg stable elements theorem and construct a Lyndon–Hochschild–Serre type spectral sequence for pro-fusion systems. As an application, we determine continuous mod-[Formula: see text] cohomology ring of [Formula: any odd prime text].

The present paper grew up from a question posed to the author by B. Feigin: ”Why does the Todd class look like the invariant volume form on a Lie group?” The answer is in a sense contained in the proof of proposition 6. In the first part we develop a formalism describing the Atiyah class, Hochschild cohomology and homology and relations between them. Essentially we introduce a global analog of ...

Let A be a finite dimensional, unital, and associative algebra which is endowed with a non-degenerate and invariant inner product. We give an explicit description of an action of cyclic Sullivan chord diagrams on the normalized Hochschild cochain complex of A. As a corollary, the Hochschild cohomology of A becomes a Frobenius algebra which is endowed with a compatible BV operator. If A is also ...

We identify the periodic cyclic homology of the algebra of complete symbols on a differential groupoid G in terms of the cohomology of S * (G), the cosphere bundle of A(G), where A(G) is the Lie algebroid of G. We also relate the Hochschild homology of this algebra with the homogeneous Poisson homology of the space A * (G) 0 ∼ = S * (G) × (0, ∞), the dual of A(G) with the zero section removed. ...

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...

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 ...