2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33363The 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 IMRNDifferential Geometrytext