Real $K$-homology of complex projective spaces

Atsushi Yamaguchi
2007 Journal of Mathematics of Kyoto University  
Thus the KO-spectrum KO = (ε n : SKO n → KO n+1 ) n∈Z is given as follows. We also recall that K * = Z[t, t −1 ], KO * = Z[α, x, y, y −1 ]/(2α, α 3 , αx, x 2 − 4y), where t, α, x and y are genetators of K −2 = π 2 (K) ∼ = Z, KO −1 = π 1 (KO) ∼ = Z/2Z, KO −4 = π 4 (KO) ∼ = Z, KO −8 = π 8 (KO) ∼ = Z. Note that t, α are the homotopy classes of the inclusion maps S 2 = CP 1 → BU = K 0 , S 1 = RP 1 → BO = KO 0 to the bottom cells.
doi:10.1215/kjm/1250281076 fatcat:vpv44bhr3zc6blfqwrha76hg7a