Hurewicz theorem

This fact is related to: homotopy groups

Statement

If $X$ is a $n$-connected space with $n\ge 2$ (viz its first $n$ homotopy groups vanish) then the Hurewicz map on the $(n+1{)}^{th}$ homotopy group is an isomorphism:

${\pi }_{n+1}(X,x_0)\to {\tilde{H}}_{n+1}(X)$

and moreover, all the reduced homology groups upto $n$ are zero.