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Let $X$ be an affine variety. My question is does there exist another affine variety with the homotopy type of the suspension of $X$?

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    $\begingroup$ It would be very helpful to know given an affine variety$X$ does there exists another affine variety $Y$ such that $H_{i+1}(Y)=H_{i}(X)$? $\endgroup$
    – rumpi123
    Commented Aug 8, 2021 at 16:21

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