Cohomology of groups of diffeomorphims related to the modules of differential operators on a smooth manifold

Abstract

Let $M$ be a manifold and $T^{\ast }M$ be the cotangent bundle. We introduce a 1-cocycle on the group of diffeomorphisms of $M$ with values in the space of linear differential operators acting on $C^{\infty }(T^{\ast }M).$ When $M$ is the $n$-dimensional sphere, $S^n$, we use this 1-cocycle to compute the first-cohomology group of the group of diffeomorphisms of $S^n$, with coefficients in the space of linear differential operators acting on contravariant tensor fields.

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References in corpus (4)

• Three Cocycles on $\Diff(S^1)$ Generalizing the Schwarzian Derivative
• Schwarzian derivative related to modules of differential operators on a locally projective manifold
• Projectively Equivariant Quantization Map
• Cohomology of the vector fields Lie algebra and modules of differential operators on a smooth manifold