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.
|Number of pages||75|
|Journal||International mathematics research notices|
|Early online date||15 Feb 2021|
|Publication status||Published - 1 Jul 2022|
- 1.01 MATHEMATICS