E. Swenson: Splitting Theorems and the JSJ: A survey

Abstract: Given a group $G$ and a (nice) class $C$ of groups. We look at the splittings of $G$ over elements of $C$. We attempt to address the following two questions: Is there a nontrivial splitting of $G$ over an element of $C$? Can we understand all splittings of $G$ over elements of $C$?