 Hurewicz theorem

If a path-connected space is $(n-1)$-connected for $n\ge 2$, then its first potentially nonzero homotopy group maps isomorphically to homology:

Hurewicz's theorem is a result in algebraic topology that pertains to the relationship between the homology and homotopy groups of a space. It specifically addresses the connection between the homology of a space and its fundamental group, particularly for spaces with certain properties.