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May 13, 2020 at 17:39 comment added Peter May I agree. I gave a new proof of the splitting priniciple in math.uchicago.edu/~may/PAPERS/Split.pdf that emphasizes that point of view.
May 13, 2020 at 0:47 comment added Troshkin Michael I like to imagine that these maps are part of the explanation of splitting principle, since $BT^n$ and $B(C_2)^n$ are classifying spaces for split bundles. This makes generators of their cohomology a sort of "universal Chern roots".
May 11, 2020 at 4:14 history answered Peter May CC BY-SA 4.0