Hi, I am trying to show that ## \mathbb CP^4 ## and ## \mathbb CP^2 \times \mathbb CP^2 ## are not homeomorphic. None of the standard methods --comparing the fundamental group of the product with the product(adsbygoogle = window.adsbygoogle || []).push({});

of fundamental groups, nor (co)homology seem to work. So I am trying to work with the cup products and

show these are different. Please let me know if this is correct: we need to compute the cohomology groups on

each side, and then we just compute all possible cup products using Kunneth's formula. Is this correct?

Thanks.

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# Non-homeomorphis between CP^4 and CP^2 x CP^2

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