|
On the continuous cohomology of diffeomorphism groups
M. V. Losik Saratov State University, Saratov, Russia
Abstract:
Suppose that MM is a connected orientable nn-dimensional manifold and m>2nm>2n. If Hi(M,R)=0 for i>0, it is proved that for each m there is a monomorphism Hm(Wn,O(n))→Hmcont(DiffM,R). If M is closed and oriented, it is proved that for each m there is a monomorphism Hm(Wn,O(n))→Hm−ncont(Diff+M,R), where 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
|
Statistics & downloads: |
Abstract page: | 258 | References: | 66 |
|