1-cocycles on the group of diffeomorphisms (Q1296412)

For a metrisable C\(^\infty\) manifold \(M\) let Diff\(_0(M)\) denote the group of all C\(^\infty\)-diffeomorphisms of \(M\) with compact support. It is shown how to think of Diff\(_0(M)\) as an infinite dimensional Lie group. After considering how to construct a differential representation associated with a given representation of Diff\(_0(M)\) the author goes on to characterise continuous 1-cocycles defined on \(M\times\text{Diff}_0(M)\).