Pullback (differential geometry)

Let ϕ : M → N {\displaystyle \phi :M\to N} be a smooth map between smooth manifolds M {\displaystyle M} and N {\displaystyle N} . Then there is an associated linear map from the space of 1-forms on N {\displaystyle N} (the linear space of sections of the cotangent bundle) to the space of 1-forms on M {\displaystyle M} .