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

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

2001-09-05

arxiv.org/abs/math/0109031v3

J. Nonlinear Math. Phys., volume 9, no. 4 (2002) 455-463

Mathematics

Differential Geometry

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Scientific paper

Let $M$ be a manifold and $T^*M$ 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 $C^{\infty} (T^*M).$ 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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