New answers tagged topological-k-theory
No, it is not. Recall that by the Chern character isomorphism, rational K-theory is periodic rational cohomology, so the cup product on odd rational K-theory doesn't vanish in any situation where the cup product on odd rational cohomology doesn't vanish; the simplest example is $S^1 \times S^1$. The stability argument is irrelevant because the cup product ...
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