  We consider intersecting hypersurfaces in curved spacetime with gravity
governed by a class of actions which are topological invariants in lower
dimensionality. Along with the Chern-Simons boundary terms there is a sequence
of intersection terms that should be added in the action functional for a well
defined variational principle. We construct them in the case of Characteristic
Classes, obtaining relations which have a general topological meaning. Applying
them on a manifold with a discontinuous connection 1-form we obtain the gravity
action functional of the system and show that the junction conditions can be
found in a simple algebraic way. At the sequence of intersections there are
localised independent energy tensors, constrained only by energy conservation.
We work out explicitly the simplest non trivial case.
