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existence Existence of an affine variety with homotopy type of suspension of another affine variety

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

existence of an affine variety with homotopy type of suspension of another affine variety

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

Existence of an affine variety with homotopy type of suspension of another affine variety

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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