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I'm trying to understand $\Sigma\mathbb{R}P^n$ so I can compute it's cohomology ring mod 2 coefficients.

I find it hard to do so since I'm not familiar with suspension, I know how $H^*(\mathbb{R}P^n, \mathbb{F}_2)$ looks like but I don't know how to link them.

clem2005
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  • Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. – Community Dec 17 '23 at 16:22
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    This may be more or less a duplicate of https://math.stackexchange.com/q/1006969/42781 or https://math.stackexchange.com/q/1322170/42781 or https://math.stackexchange.com/q/2964758/42781. – John Palmieri Dec 17 '23 at 17:36
  • the mulptiplicative structure is trivial on reduced cohomology (which you can show for the suspension on anything) and on abelian groups, the suspension isomorphism will answer your question more generally. As a warmup, take $n=1$ and try excision. – Andres Mejia Jan 08 '24 at 20:06

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