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For questions about ring spectra (in homotopy theory).
15
votes
Accepted
$KO_*$ groups of $\mathbb{R}P^\infty$, "Snaiths" theorem for $KO$
There are many ways to do this. One elementary approach is to use the Adams spectral sequence
$Ext_A(H^*ko \wedge RP^\infty, F_2) \cong Ext_{A(1)}(H^*RP^\infty,F_2) \Rightarrow ko_*(RP^\infty) $ …