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Nov 16, 2019 at 0:35 comment added user131113 @Bertram yes, of course, but how does it help?
Nov 14, 2019 at 8:20 comment added Bertram Arnold You still have maps $(CP^\infty)^{\wedge n}\to MSU$ given as the Thomification of the stable bundle $L_1\oplus\cdots\oplus L_n + L_1^\vee\otimes\cdots\otimes L_n^\vee - (n+1)$ (i.e. the classifying map of the maximal torus $U(1)^n\to SU(n+1)$). Their pullbacks are jointly injective on cohomology.
Nov 14, 2019 at 6:25 history asked user131113 CC BY-SA 4.0