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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.
Received: May 25, 2009
Citation:
M. V. Losik, “On the continuous cohomology of diffeomorphism groups”, Mosc. Math. J., 10:2 (2010), 377–397
Linking options:
https://www.mathnet.ru/eng/mmj385 https://www.mathnet.ru/eng/mmj/v10/i2/p377
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Abstract page: | 228 | References: | 48 |
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