Open 𝑟-Spin Theory I: Foundations. (15th February 2021)

• Record Type: Journal Article
• Authors: Buryak, Alexandr; Clader, Emily; Tessler, Ran J
• Is Part Of: International mathematics research notices. Volume 2022:Number 14(2022)
• Page Start: 10458
• Page End: 10532
• Publication Date: 2021-02-15
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnaa345
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: We lay the foundation for a version of $r$ -spin theory in genus zero for Riemann surfaces with boundary. In particular, we define the notion of $r$ -spin disks, their moduli space, and the Witten bundle; we show that the moduli space is a compact smooth orientable orbifold with corners, and we prove that the Witten bundle is canonically relatively oriented relative to the moduli space. In the sequel to this paper, we use these constructions to define open $r$ -spin intersection theory and relate it to the Gelfand–Dickey hierarchy, thus providing an analog of Witten's $r$ -spin conjecture in the open setting.