Three Cocycles on $\Diff(S^1)$ Generalizing the Schwarzian Derivative

Abstract

The first group of differentiable cohomology of $\Diff(S^1)$, vanishing on the Möbius subgroup $PSL(2,R)\subset\Diff(S^1)$, with coefficients in modules of linear differential operators on $S^1$ is calculated. We introduce three non-trivial $PSL(2,R)$-invariant 1-cocycles on $\Diff(S^1)$ generalizing the Schwarzian derivative.

18 pages, LaTex. to appear in IMRN

Cited by in corpus (5)

• Cohomology of the Lie Superalgebra of Contact Vector Fields on ${\mathbb{R}}^{1|1}$ and Deformations of the Superspace of Symbols
• Schwarzian derivative related to modules of differential operators on a locally projective manifold
• sl(2)-Trivial Deformations of Vect_{Pol}(R)-Modules of Symbols
• On sl(2)-equivariant quantizations
• Cohomology of groups of diffeomorphims related to the modules of differential operators on a smooth manifold