  Gravity in d dimensions is formulated as the gauge theory of local SO(2,d-1)
gauge group. The Chern-Pontryagin index ${\cal P}_{2n}$ plays a crucial role in
both gravity and gauge theories. ${\cal P}_{2n}(gravity)$ gives the
gravitational Lagrangian in 2n dimensions, having the vacuum solution
$AdS_{2n}$. The same but global symmetry is shared with the gauge theories and
0,1-cochains of the Chern-Simon index ${\cal C}_{2n}(gauge)$ take part of
$CFT_{2n-1}$ and $CFT_{2n-2}$, respectively. Gravity in odd dimensions is quite
analogously formulated to that in even dimensions. This gives new insights on
AdS/CFT correspondence.
