Let $Y$ be a CW-complex and $X$ its universal cover. Could you give me a proof (or a referece) for the following fact:
$X$ is contractible $\Leftrightarrow$ $H_i(X)=0$ $\forall i\geq2$ $\Leftrightarrow$ $\pi_iY=0$ $\forall i\geq2$.
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3 years ago