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Results tagged with cohomology-operations
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user 21564
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When the Pontryagin square is an even class?
If $B \in H^2(X;\mathbb{Z}_2)$ satisfies $B^2 \neq 0$, then $\mathfrak{P}(B) \in H^4(X; \mathbb{Z}_4)$ is not even as $\mathfrak{P}(B) \equiv B^2 \bmod 2$. Such classes can exist on spin manifolds, fo …
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