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Homotopy theory, homological algebra, algebraic treatments of manifolds.

10 votes
5 answers
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Is a map a homotopy equivalence if its suspension is so?

Exist simply connected CW complexes $X$, $Y$ and a mapping $f:X\to Y$ with the property that the reduced suspension $\Sigma f:\Sigma X\to\Sigma Y$ is a homotopy equivalence but $f$ is not?
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