Suppose the group $G$ splits as the amalgamated product $A\ast_CB$ (with all groups finitely generated). The Cayley graph of $G$ with respect to an appropriate generating set has two ``halfspaces", one on the $A$-"side" of $C$ and the other on the $B$-"side" of $C$. We show that under mild (accessibility) conditions on $C$ that if $G$ is one-ended, then this splitting can be upgraded to a graph of groups decomposition of $G$ such that halfspaces associated to any edge group are one-ended. We will focus on a second result that states: If a one-ended finitely presented group $G$ admits a splitting $A\ast_CB$ with one ended half spaces associated to $C$ and $C$ has more than one end, then $G$ is not 1-acyclic at infinity. In particular, $H^2(G,\mathbb ZG)\ne 0$ (so that $G$ is not a duality group) and $G$ is not simply connected at infinity. This work is joint with Sam Shepherd.