Characteristic numbers from 2-cocycles on formal groups (Q1612148)

Let \(E\) be a complex oriented (co)homology theory. The author gives explicit polynomial generators \(\alpha_i, i=2,3, \ldots \) of the ring \(E_*(BSU)=\pi_8(E)[\alpha_2, \alpha _3,\ldots]\). The author also gives certain explicit polynomial generators of the ring \(K_*(B\operatorname {Spin};\mathbb Z/2)\). Basing on this, the author gives a new proof of a theorem of \textit{M. Ando, M. J. Hopkins} and \textit{N. P. Strickland} [Elliptic spectra, the Witten genus and the theorem of the cube. Invent. Math. 146, No. 3, 595-687 (2001; Zbl 1031.55005)] that \(K_*(B\operatorname {Spin};\mathbb Z/2)\) carries the universal real symmetric 2-cocycle for the multiplicative formal group.