On certain cases of Seifert Van Kampen Given two connected open sets $U,V \subset X$ such that $U \cap V$ is path connected and $U \cup V = X$, then $\pi_1(U) \ast_{\pi_1(U \cap V)} \pi_1(V) \cong \pi_1(X)$. This is of course the Seifert Van Kampen theorem, a question in Munkres asks if the homomorphism induced by the inclusion map of $i: V \rightarrow X$ is trivial what can you say about the homomorphism induced by $j: U \rightarrow X$.
It's clear to me that $j_\ast$ must be surjective and therefore $\pi_1(X) \cong \pi_1(U)/ker(j_\ast)$. My question is can you say anything more? Does the kernel of $j_\ast$ relate at all to $F$, as given in the usual diagram. Would the kernel be at all related to the normal closure of the image of the induced homomorphism of the inclusion $k: U \cap V \rightarrow U$?

Notice that the question is purely algebraic. If $G=\pi_1(U)$, $G'=\pi_1(V)$ and $H=\pi_1(U\cap V)$, you are asking what is the kernel of the obvious map $G\to G*_HG'$ (where the amalgamation happens along the images of $H$ in $G$ and $G'$) if the map $G'\to G*_HG'$ is trivial. 
