Six Dimensional Topological Gravity and the Cosmological Constant Problem

We formulate a topological theory in six dimensions with gauge group SO(3,3) which reduces to gravity on a four dimensional defect if suitable boundary conditions are chosen. In such a framework we implement the reflection automorphism of SO(3,3) as a $\Z2$ symmetry which forbids the appearance of a gravitational cosmological constant. Some temptative speculations are presented also for the possible inclusion of the matter contribution at a full quantum level.