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 ∞(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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics