Or similarly, given the cohomology ring of a space, is it possible to compute its cohomology groups? I'm mainly interested in integer and mod 2 homology and cohomology.
2026-04-02 07:25:15.1775114715
Is it possible to compute homology groups of a space given the Pontryagin ring?
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If you know the Pontryagin ring $H_*(X ; \mathbb{Z})$ of the $H$-space $X$, then you automatically know $H_n(X; \mathbb{Z})$ for all $n$ as $H_n(X; \mathbb{Z})$ is merely the $n$th graded component of $H_*(X;\mathbb{Z})$. Then you can use Universal Coefficients to determine $H_n(X; A)$ for any abelian group $A$.