  Starting from a relativistic phenomenology of anyons in crystals, we discuss
the concept of relativistic interaction and the need to unify electromagnetism
and gravitation within the Spencer cohomology of Lie equations. Then, from the
sophisticated non-linear Spencer complex of the Poincar\'e and conformal Lie
pseudogroups, we build up a non-linear relative complex assigned to a gauge
sequence for electromagnetic and gravitational potentials and fields. Then,
using a conformally equivariant Lagrangian density, we deduce, first, the two
first steps of its corresponding Janet complex and second, the dual relative
linear complex. We conclude by giving suggestions for higher unification with
the weak and strong interactions and interpretations of the Lagrangian density
as a thermodynamical function and quantum wave-function.
