  Black holes in anti de Sitter (AdS) spacetimes undergo phase transitions
which typically lead to the existence of critical points, that can be
classified using topological techniques. Availing the Bragg-Williams
construction which provides an off-shell free energy formalism, we compute the
topological charge of the Hawking-Page (HP) transition for Einstein-Born-Infeld
black holes in anti de Sitter spacetime and match the result with the
confinement-deconfinement transition in the dual gauge theory, which turn out
to be in perfect agreement.
