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

Mathematics – Differential Geometry

Scientific paper

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18 pages, LaTex. to appear in IMRN

Scientific paper

The first group of differentiable cohomology of $\Diff(S^1)$, vanishing on
the M\"obius 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.

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