Open r-spin theory I: Foundations

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 analogue of Witten's $r$-spin conjecture in the open setting.

The content of this paper was included in the content of the first versions (v1-v3) of arXiv:1809.02536, before we splitted it. It includes the definition of r-spin disks, the construction of the moduli spaces and bundles, and the proofs of orientation theorems

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Cited by in corpus (1)

• Higher Airy structures and topological recursion for singular spectral curves