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Ola Sande
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Numerator in the zeta values at negative odd integers

The real J-homomorphism produces cyclic subgroups of size the denominator of $\zeta(1-2k)=-B_{2k}/k$ for $k>0$ in $\pi_{4k-1}S$ which completely account for first layer of the chromatic filtration on $\pi_*S$.

Question: Does the numerator in $\zeta(1-2k)$ also relate to $\pi_*S$ (at higher layers in the chromatic filtration)?

Quess: Can we think of denominator of $\zeta(1-2k)$ as local information (since it is hit by the J-homomorphism) and the numerator of $\zeta(1-2k)$ as global information?

Ola Sande
  • 705
  • 7
  • 17