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THE SPECTRAL CURVE OF THE EYNARDORANTIN RECURSION VIA THE LAPLACE TRANSFORM
"... Abstract. The EynardOrantin recursion formula provides an effective tool for certain enumeration problems in geometry. The formula requires a spectral curve and the recursion kernel. We present a uniform construction of the spectral curve and the recursion kernel from the unstable geometries of th ..."
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Cited by 9 (2 self)
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Abstract. The EynardOrantin recursion formula provides an effective tool for certain enumeration problems in geometry. The formula requires a spectral curve and the recursion kernel. We present a uniform construction of the spectral curve and the recursion kernel from the unstable geometries of the original counting problem. We examine this construction using four concrete examples: Grothendieck’s dessins d’enfants (or highergenus analogue of the Catalan numbers), the intersection numbers of tautological cotangent classes on the moduli stack of stable pointed curves, single Hurwitz numbers, and the stationary GromovWitten invariants of the complex projective line. Contents
A generalized topological recursion for arbitrary ramification
, 2012
"... Abstract: The EynardOrantin 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 va ..."
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Cited by 7 (1 self)
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Abstract: The EynardOrantin 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. We check in various examples that our generalized recursion is compatible with invariance of the free energies under the transformation (x, y) 7 → (y, x), where either x or y (or both) have higher order ramification, and that it satisfies some of the most important properties of the original recursion. Along the way, we show that invariance under (x, y) 7 → (y, x) is in fact more subtle than expected; we show that there exists a number of counter examples, already in the case of the original EynardOrantin recursion, that deserve further study. ar X iv
Topological recursion for chord diagrams, RNA complexes, and cells in moduli spaces
 Nucl. Phys. B
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