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Yasha
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Chern numbers of primitve classes in BU

How does one compute Chern numbers of spherical rational homology classes $$f: S ^{2k} \to BU.$$ These generate rational homology by Milnor-Moore theorem since BU is a connected H-space, and so c_k cannot kill such a class. It seems very likely that $\langle c_k,[f] \rangle =1$ but what is the proof?

Yasha
  • 491
  • 3
  • 9