  Thermodynamics of black holes in anti de Sitter (AdS) spacetimes typically
contains critical points in the phase diagram, some of which correspond to the
first order transition ending in a second order one. Following the recent
proposal in [arXiv:2112.01706] on using Duan's $\phi$-mapping theory, we
classify the critical points of six dimensional charged Gauss-Bonnet black
holes in AdS spacetime. We find that the higher derivative corrections from
Gauss-Bonnet gravity do not change the topological class of critical points in
charged black holes in AdS, unlike the case of Born-Infeld corrections noted
earlier. The connection between the topological nature of critical points and
existence of first order phase transitions breaks down in a certain parameter
regime. A resolution is proposed by treating the novel and conventional
critical points as phase creation and phase annihilation points, respectively.
Examples are provided to support the proposal.
