I have the following question, which I dont really know if its true: Let $g : X \rightarrow Y$ be a continous map between two closed, oriented $n-$dimensional manifolds such that $g^{*} : H^{n}(Y, \mathbb{Q}) \rightarrow H^{n}(X, \mathbb{Q})$ is non-zero (here in this case we have $H^{n}(X, \mathbb{Q}) = \mathbb{Q}$ and $H^{n}(Y, \mathbb{Q}) = \mathbb{Q}$). How can one show that the map $g^{*} : H^{k}(Y, \mathbb{Q}) \rightarrow H^{k}(X, \mathbb{Q})$ is injective for $k
ronald