On the continuous cohomology of diffeomorphism groups
M.V.Losik

TL;DR
This paper establishes monomorphisms from certain cohomology groups related to the Weil algebra into the continuous cohomology of diffeomorphism groups of manifolds, revealing new connections between geometric structures and group cohomology.
Contribution
It proves the existence of monomorphisms from $H^m(W_n,O(n))$ into the continuous cohomology of diffeomorphism groups under specific conditions, extending understanding of their cohomological properties.
Findings
Monomorphism from $H^m(W_n,O(n))$ to $H^m_{cont}(Diff M, R)$ for manifolds with trivial higher cohomology.
Monomorphism from $H^m(W_n,O(n))$ to $H^{m-n}_{cont}(Diff_+ M, R)$ for closed oriented manifolds.
Results connect algebraic cohomology of Lie algebras with the topology of diffeomorphism groups.
Abstract
Suppose that is a connected orientable -dimensional manifold and . If for , it is proved that for each there is a monomorphism . If is closed and oriented, it is proved that for each there is a monomorphism , where is a group of preserving orientation diffeomorphisms of .
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometric and Algebraic Topology · Advanced Differential Equations and Dynamical Systems
