Open \(r\)-spin theory. II: The analogue of Witten's conjecture for \(r\)-spin disks
type: Item
instance of: scholarly article
title: Open \(r\)-spin theory. II: The analogue of Witten's conjecture for \(r\)-spin disks
zbMATH Open document ID: 1547.14061
author: A. Buryak
author: Emily Clader
author: Ran J. Tessler
published in: Journal of Differential Geometry
publication date: 2024-08-27T00:00:00Z
review text: The paper under review forms part of a series of three articles devoted to the construction of \(r\)-spin theory for Riemann surfaces with boundary. Part I was published in [Int. Math. Res. Not. 2022, No. 14, 10458--10532 (2022; Zbl 1504.14078)], and Part III in [J. Geom. Phys. 192, Article ID 104960, 12 p. (2023; Zbl 1523.14009)].\N\NLet \((C;z_1, \dots , z_n)\) be a smooth marked curve. Then, an \(r\)-spin structure is a line bundle \(S\) together with an isomorphism \(S^{\otimes r} \approx \omega_C(- \sum_{i=1}^n a_i[z_i])\), where \(a_i \in \{0,1, \dots ,r-1\}\). In Part I the authors gave the foundation for an \(r\)-spin theory in genus zero for Riemann surfaces with boundary. The authors restricted themselves in that paper to such surfaces in which each connected component has genus zero.\N\NIn the present paper, they define open \(r\)-spin intersection numbers and prove topological recursion relations that these numbers satisfy. Then these relations are used to prove the main results, Theorems 1.1, 1.2 and 1.4, which provide the open \(r\)-spin version of Witten's conjecture in genus zero. So, this paper concludes the construction for genus zero.\N\NIn Part III, which in fact appeared earlier, the authors study the extension of these results to higher genus.
reviewed by: José Javier Etayo
Mathematics Subject Classification ID: 14J80
Mathematics Subject Classification ID: 30F99
Mathematics Subject Classification ID: 53C27
zbMATH DE Number: 7902284
zbMATH Keywords: r-spin theory
zbMATH Keywords: moduli space
zbMATH Keywords: orientable orbifold
zbMATH Keywords: Witten bundle
MaRDI profile type: Publication
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DOI: 10.4310/JDG/1721075259
description: scientific article; zbMATH DE number 7902284