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added missing hypothesis
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YCor
YCor
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Simply connected finite CW-complex with only finitely many nontrivial homotopy and homology groups

Let $X$ be a simply connected finite CW-complex such that all but finitely many of its homotopy groups and its homology groups (with $\mathbb Z$ coefficients) are 0.

Is $X$ then necessarily contractible?

I do not really believe that this is true; but I was also not able to construct a counterexample.

Simply connected CW-complex with only finitely many nontrivial homotopy and homology groups

Let $X$ be a simply connected CW-complex such that all but finitely many of its homotopy groups and its homology groups (with $\mathbb Z$ coefficients) are 0.

Is $X$ then necessarily contractible?

I do not really believe that this is true; but I was also not able to construct a counterexample.

Simply connected finite CW-complex with only finitely many nontrivial homotopy and homology groups

Let $X$ be a simply connected finite CW-complex such that all but finitely many of its homotopy groups and its homology groups (with $\mathbb Z$ coefficients) are 0.

Is $X$ then necessarily contractible?

I do not really believe that this is true; but I was also not able to construct a counterexample.

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Jens Reinhold
Jens Reinhold
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Simply connected CW-complex with only finitely many nontrivial homotopy and homology groups

Let $X$ be a simply connected CW-complex such that all but finitely many of its homotopy groups and its homology groups (with $\mathbb Z$ coefficients) are 0.

Is $X$ then necessarily contractible?

I do not really believe that this is true; but I was also not able to construct a counterexample.