Topological recursion with hard edges

Chekhov, Leonid; Norbury, Paul

doi:10.1142/s0129167x19500149

Cited by 23 publications

(35 citation statements)

References 37 publications

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“…Example 4 Chekhov and Norbury [13] consider topological recursion applied to the spectral curve x 2 y 2 − 4y 2 − 1 = 0 given by the rational parametrisation…”

Section: Topological Recursionmentioning

confidence: 99%

Generalisations of the Harer–Zagier recursion for 1-point functions

Chaudhuri

2021

J Algebr Comb

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Harer and Zagier proved a recursion to enumerate gluings of a 2d-gon that result in an orientable genus g surface, in their work on Euler characteristics of moduli spaces of curves. Analogous results have been discovered for other enumerative problems, so it is natural to pose the following question: how large is the family of problems for which these so-called 1-point recursions exist? In this paper, we prove the existence of 1-point recursions for a class of enumerative problems that have Schur function expansions. In particular, we recover the Harer-Zagier recursion, but our methodology also applies to the enumeration of dessins d'enfant, to Bousquet-Mélou-Schaeffer numbers, to monotone Hurwitz numbers, and more. On the other hand, we prove that there is no 1-point recursion that governs single Hurwitz numbers. Our results are effective in the sense that one can explicitly compute particular instances of 1-point recursions, and we provide several examples. We conclude the paper with a brief discussion and a conjecture relating 1-point recursions to the theory of topological recursion.

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“…Example 4 Chekhov and Norbury [13] consider topological recursion applied to the spectral curve x 2 y 2 − 4y 2 − 1 = 0 given by the rational parametrisation…”

Section: Topological Recursionmentioning

confidence: 99%

Generalisations of the Harer–Zagier recursion for 1-point functions

Chaudhuri

2021

J Algebr Comb

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“…It arises out of topological recursion applied to the spectral curve (x, y) = ( 1 2 z 2 , 1/z) [9] and more generally to any spectral curve with points locally of this form near a zero of dx, [7].…”

Section: 22mentioning

confidence: 99%

“…k1,...,kn M g,n to the specialization ǫ = −1 in(7)). It turns out that the monotone Hurwitz numbers are governed by the very same topological recursion with a special choice of the expansion point z = 1 and the local coordinate X at this point defined by the change z = √ 1 − 4X.Proposition 5.9 ([10]).…”

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confidence: 99%

Polynomial relations among kappa classes on the moduli space of curves

Kazarian¹,

Norbury²

2021

Preprint

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“…We assume that the function y is meromorphic in the neighbourhoods of the zeros of dx. We allow the spectral curve to be irregular [CN19], that is, the poles of y may coincide with the zeroes of dx.…”

Section: Tau-functions Identification and Topological Recursionmentioning

confidence: 99%

KP integrability of triple Hodge integrals. III. Cut-and-join description, KdV reduction, and topological recursions

Alexandrov

2021

Preprint

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In this paper, we continue our investigation of the triple Hodge integrals satisfying the Calabi-Yau condition. For the tau-functions, which generate these integrals, we derive the complete families of the Heisenberg-Virasoro constraints. We also construct several equivalent versions of the cut-and-join operators. These operators describe the algebraic version of topological recursion. For the specific values of parameters associated with the KdV reduction, we prove that these tau-functions are equal to the generating functions of intersection numbers of ψ and κ classes. We interpret this relation as a symplectic invariance of the Chekhov-Eynard-Orantin topological recursion and prove this recursion for the general Θ-case.

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Topological recursion with hard edges

Cited by 23 publications

References 37 publications

Generalisations of the Harer–Zagier recursion for 1-point functions

Generalisations of the Harer–Zagier recursion for 1-point functions

Polynomial relations among kappa classes on the moduli space of curves

KP integrability of triple Hodge integrals. III. Cut-and-join description, KdV reduction, and topological recursions

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