Search results for "Equivariant cohomology"
showing 4 items of 14 documents
Chevalley cohomology for aerial Kontsevich graphs
2013
Let $T_{\operatorname{poly}}(\mathbb{R}^d)$ denote the space of skew-symmetric polyvector fields on $\mathbb{R}^d$, turned into a graded Lie algebra by means of the Schouten bracket. Our aim is to explore the cohomology of this Lie algebra, with coefficients in the adjoint representation, arising from cochains defined by linear combination of aerial Kontsevich graphs. We prove that this cohomology is localized at the space of graphs without any isolated vertex, any "hand" or any "foot". As an application, we explicitly compute the cohomology of the "ascending graphs" quotient complex.
Holomorphic de Rham Cohomology
2017
We are going to define a natural comparison isomorphism between algebraic de Rham cohomology and singular cohomology of varieties over the complex numbers with coefficients in \(\mathbb {C}\). The link is provided by holomorphic de Rham cohomology, which we study in this chapter.
Closed star products and cyclic cohomology
1992
We define the notion of a closed star product. A (generalized) star product (deformation of the associative product of functions on a symplectic manifold W) is closed iff integration over W is a trace on the deformed algebra. We show that for these products the cyclic cohomology replaces the Hochschild cohomology in usual star products. We then define the character of a closed star product as the cohomology class (in the cyclic bicomplex) of a well-defined cocycle, and show that, in the case of pseudodifferential operators (standard ordering on the cotangent bundle to a compact Riemannian manifold), the character is defined and given by the Todd class, while in general it fails to satisfy t…
Hochschild Cohomology Theories in White Noise Analysis
2008
We show that the continuous Hochschild cohomology and the differential Hochschild cohomology of the Hida test algebra endowed with the normalized Wick product are the same.