  We formulate a notion of abstract loop equations, and show that their
solution is provided by a topological recursion under some assumptions, in
particular the result takes a universal form. The Schwinger-Dyson equation of
the one and two hermitian matrix models, and of the O(n) model appear as
special cases. We study applications to repulsive particles systems, and
explain how our notion of loop equations are related to Virasoro constraints.
Then, as a special case, we study in detail applications to enumeration
problems in a general class of non-intersecting loop models on the random
lattice of all topologies, to SU(N) Chern-Simons invariants of torus knots in
the large N expansion. We also mention an application to Liouville theory on
surfaces of positive genus.
