On the continuous cohomology of diffeomorphism groups

M. V. Losik

Published 2009-06-25Version 1

Suppose that $M$ is a connected orientable $n$-dimensional manifold and $m>2n$. If $H^i(M,\R)=0$ for $i>0$, it is proved that for each $m$ there is a monomorphism $H^m(W_n,\on{O}(n))\to H^m_{\on{cont}}(\on{Diff}M,\R)$. If $M$ is closed and oriented, it is proved that for each $m$ there is a monomorphism $H^m(W_n,\on{O}(n))\to H^{m-n}_{\on{cont}}(\on{Diff}_+M,\R)$, where $\on{Diff}_+M$ is a group of preserving orientation diffeomorphisms of $M$.