  We extend our topological renormalization scheme for Entanglement Entropy to
holographic CFTs of arbitrary odd dimensions in the context of the AdS/CFT
correspondence. The procedure consists in adding the Chern form as a boundary
term to the area functional of the Ryu-Takayanagi minimal surface. The
renormalized Entanglement Entropy thus obtained can be rewritten in terms of
the Euler characteristic and the AdS curvature of the minimal surface. This
prescription considers the use of the Replica Trick to express the renormalized
Entanglement Entropy in terms of the renormalized gravitational action
evaluated on the conically-singular replica manifold extended to the bulk. This
renormalized action is obtained in turn by adding the Chern form as the
counterterm at the boundary of the 2n-dimensional asymptotically AdS bulk
manifold. We explicitly show that, up to next-to-leading order in the
holographic radial coordinate, the addition of this boundary term cancels the
divergent part of the Entanglement Entropy. We discuss possible applications of
the method for studying CFT parameters like central charges.
