Résumé
Gopakumar, Ooguri and Vafa famously proposed the existence of a correspondence between a topological gauge theory – U (N) Chern–Simons theory on the three-sphere – on one hand, and a topo-logical string theory – the topological A-model on the resolved conifold – on the other. On the physics side, this duality provides a concrete instance of the large N gauge/string correspondence where exact computations can be performed in detail; mathematically, it puts forward a triangle of striking relations between quantum invariants (Reshetikhin–Turaev–Witten) of knots and 3-manifolds, curve-counting invari-ants (Gromov–Witten/Donaldson–Thomas) of local Calabi-Yau 3-folds, and the Eynard–Orantin recursion for a specific class of spectral curves. I here survey recent results on the most general frame of validity of the strongest form of this correspondence and discuss some of its implications.