On the continuous cohomology of diffeomorphism groups

2009/06/25 by Losik, M. V.
#22E41 #58D05 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0906.4693

Abstract

Suppose that M is a connected orientable n-dimensional manifold and m>2n. If Hⁱ(M,\R)=0 for i>0, it is proved that for each m there is a monomorphism H^m(W_n,\onO(n))→ H^m_\oncont(\onDiffM,\R). If M is closed and oriented, it is proved that for each m there is a monomorphism H^m(W_n,\onO(n))→ H^m-n_\oncont(\onDiff₊M,\R), where \onDiff₊M is a group of preserving orientation diffeomorphisms of M.

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