Can we say some thing about maps on Cohomology of two surfaces, provided we have only intersection form Matrix?
Say, I have intersection matrices for $H^1(X,G) \otimes H^1(X,G) \rightarrow H^2(X,G)$ and $H^1(Y,G) \otimes H^1(Y,G) \rightarrow H^2(Y,G)$
Can I say some thing (atleast existence of a non trivial map or no non trivial map exists) about $H^2(Y,G) \rightarrow H^2(X,G)$ assuming I have a map from $X \rightarrow Y$.
Independent of all the other stuff, $f^*$ gives the map, and, for $G=\Bbb Z$, it is given by $\text{deg}(f)$.