  In two previous papers, we exposed a combinatorial approach to the program of
Geometry of Interaction, a program initiated by Jean-Yves Girard. The strength
of our approach lies in the fact that we interpret proofs by simpler structures
- graphs - than Girard's constructions, while generalizing the latter since
they can be recovered as special cases of our setting. This third paper extends
this approach by considering a generalization of graphs named graphings, which
is in some way a geometric realization of a graph. This very general framework
leads to a number of new models of multiplicative-additive linear logic which
generalize Girard's geometry of interaction models and opens several new lines
of research. As an example, we exhibit a family of such models which account
for second-order quantification without suffering the same limitations as
Girard's models.
