  This paper is the fourth of a series exposing a systematic combinatorial
approach to Girard's Geometry of Interaction (GoI) program. The GoI program
aims at obtaining particular realisability models for linear logic that
accounts for the dynamics of cut-elimination. This fourth paper tackles the
complex issue of defining exponential connectives in this framework. For that
purpose, we use the notion of \emph{graphings}, a generalisation of graphs
which was defined in earlier work. We explain how to define a GoI for
Elementary Linear Logic (ELL) with second-order quantification, a sub-system of
linear logic that captures the class of elementary time computable functions.
