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A simple example is BU(1) = CP^infty, and H*(CP^infty, Z) = Z[[x]] with x in H^2. This is the first Chern class of a line bundle! More generally, BO(n) is an infinite Grassmannian, and H*(BO(n), Z/2) is the free polynomial algebra over Z/2 generated by the first n Stiefel Whitney classes.
Mar 5, 2025, 1:36 AM
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