We consider the renormalization of holographic entanglement
entropy (HEE) for Conformal Field Theories in odd dimensions, dual to
Einstein gravity with negative cosmological constant in one
dimension higher. We make explicit the equivalence between
renormalized entropy and the renormalized area of the entangling
surface. In particular, for constant-curvature surfaces, HEE is fully
determined in terms of a single topological number
(Euler characteristic).
(Based on arXiv:1712.09099, 1803.04990 and 1806.10708)