Trace Homomorphism for Smooth Manifolds
نویسنده
چکیده
Let M be a closed connected smooth manifold and G = Diff0(M) denote the connected component of the diffeomorphism group of M containing the identity. The natural action of G on M induces the trace homomorphism on homology. We show that the image of trace homomorphism is annihilated by the subalgebra of the cohomology ring of M , generated by the characteristic classes of M . Analogously, if J is an almost complex structure on M and G denotes the identity component of the group of diffeomorphisms of M preserving J then the image of the corresponding trace homomorphism is annihilated by subalgebra generated by the Chern classes of (M, J).
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