Cohomological injectivity of a degree-one map
= Cohomological injectivity of a degree-one map
A degree-one map $f:M\to N$ between closed connected oriented manifolds of the same dimension induces an injection $f^*:H^*(N;R)\to H^*(M;R)$. The wrong-way map defined using <Poincare duality> is a left inverse by the projection formula and $f_*[M]=[N]$.