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I think the answer is no, due to this answerthis answer to this questionthis question. There are Moore spaces with the same cohomology rings and module structure over the mod $p$ Steenrod algebra, which nevertheless have different homology groups and so their singular complexes cannot be weakly equivalent.

I think the answer is no, due to this answer to this question. There are Moore spaces with the same cohomology rings and module structure over the mod $p$ Steenrod algebra, which nevertheless have different homology groups and so their singular complexes cannot be weakly equivalent.

I think the answer is no, due to this answer to this question. There are Moore spaces with the same cohomology rings and module structure over the mod $p$ Steenrod algebra, which nevertheless have different homology groups and so their singular complexes cannot be weakly equivalent.

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Mark Grant
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I think the answer is no, due to this answer to this question. There are Moore spaces with the same cohomology rings and module structure over the mod $p$ Steenrod algebra, which nevertheless have different homology groups and so their singular complexes cannot be weakly equivalent.