Hebrew University topology and geometry seminar

Abstract: Model theorists define, in structures whose first-order theory is "stable" (i.e. suitably nice), a notion of independence between elements. This notion coincides for example with linear independence when the structure considered is a vector space, and with algebraic independence when it is an algebraically closed field. Sela showed that the theory of the free group is stable. In a joint work with Rizos Sklinos, we give some interpretation of this model theoretic notion of independence in the free group using cyclic JSJ decompositions. These are decompositions as graphs of groups which encode all the possible splittings of a group as amalgamated products or HNN extensions over cyclic groups.