Primary obstruction

Summary

The primary obstruction is the first obstruction that appears when one tries to extend a map into an $(n-1)$-connected space over a CW complex. It is a single cohomology class in degree $n + 1$ with coefficients in $\pi_n$ of the target, and it does not depend on any choice. Many characteristic classes, such as the Euler class of an oriented sphere bundle, are primary obstructions.