On ELSV-type formulae and relations between Ω-integrals via deformations of spectral curves

IF 1.6 3区数学 Q1 MATHEMATICS Journal of Geometry and Physics Pub Date : 2024-10-22 DOI:10.1016/j.geomphys.2024.105343

Gaëtan Borot , Maksim Karev , Danilo Lewański

引用次数: 0

Abstract

The general relation between Chekhov–Eynard–Orantin topological recursion and the intersection theory on the moduli space of curves, the deformation techniques in topological recursion, and the polynomiality properties with respect to deformation parameters can be combined to derive vanishing relations involving intersection indices of tautological classes. We apply this strategy to three different families of spectral curves and show they give vanishing relations for integrals involving Ω-classes. The first class of vanishing relations are genus-independent and generalises the vanishings found by Johnson–Pandharipande–Tseng [35] and by the authors jointly with Do and Moskovsky [8]. The two other classes of vanishing relations are of a different nature and depend on the genus.

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通过谱曲线变形论 ELSV 型公式和 Ω 积分关系

契科夫-艾纳德-奥兰汀拓扑递推与曲线模空间上的交点理论之间的一般关系、拓扑递推中的变形技术以及变形参数的多项式性质可以结合起来，推导出涉及同调类交点指数的消失关系。我们将这一策略应用于三个不同的谱曲线系列，并证明它们给出了涉及 Ω 类的积分的消失关系。第一类消失关系与种属无关，并推广了约翰逊-潘达里潘德-曾[35]以及作者与杜和莫斯科夫斯基[8]共同发现的消失关系。另外两类消失关系性质不同，取决于种属。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity

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