Trace Homomorphism for Smooth Manifolds

Details Trace Homomorphism for Smooth Manifolds Trace Homomorphism for Smooth Manifolds

2005-03-21

arxiv.org/abs/math/0503411v2

Mathematics

Geometric Topology

5 pages, minor corrections and some additions

Scientific paper

Let $M$ be a closed connected smooth manifold and $G=\textmd{Diff}_0(M)$ 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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