A generalized topological recursion for arbitrary ramification

Understand

The Eynard-Orantin topological recursion relies on the geometry of a Riemann surface S and two meromorphic functions x and y on S.

• To formulate the recursion, one must assume that x has only simple ramification points.
• In this paper we propose a generalized topological recursion that is valid for x with arbitrary ramification.
• We justify our proposal by studying degenerations of Riemann surfaces.