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Mosc. Math. J., 2010, Volume 10, Number 2, Pages 377–397 (Mi mmj385)  

On the continuous cohomology of diffeomorphism groups

M. V. Losik

Saratov State University, Saratov, Russia

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

Key words and phrases: diffeomorphism group, group cohomology, diagonal cohomology.

DOI: https://doi.org/10.17323/1609-4514-2010-10-2-377-397

Full text: http://www.ams.org/.../abst10-2-2010.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 22E41, 58D05, 57R32, 22E65, 17B66
Received: May 25, 2009
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Citation: M. V. Losik, “On the continuous cohomology of diffeomorphism groups”, Mosc. Math. J., 10:2 (2010), 377–397

Citation in format AMSBIB
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\by M.~V.~Losik
\paper On the continuous cohomology of diffeomorphism groups
\jour Mosc. Math.~J.
\yr 2010
\vol 10
\issue 2
\pages 377--397
\mathnet{http://mi.mathnet.ru/mmj385}
\crossref{https://doi.org/10.17323/1609-4514-2010-10-2-377-397}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2722803}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000279342400006}


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