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Open r-spin theory III: a prediction for higher genus
Journal of Geometry and Physics. 2023. Vol. 192. Article 104960.
In our previous two papers, we constructed an r-spin theory in genus zero for Riemann surfaces with boundary and fully determined the corresponding intersection numbers, providing an analogue of Witten's r-spin conjecture in genus zero in the open setting. In particular, we proved that the generating series of open r-spin intersection numbers is determined by the genus-zero part of a special solution of a certain extension of the Gelfand–Dickey hierarchy, and we conjectured that the whole solution controls the open r-spin intersection numbers in all genera, which do not yet have a geometric definition. In this paper, we provide geometric and algebraic evidence for the correctness of this conjecture.
Keywords: пространство модулейmoduli spaceRiemann surface with boundaryриманова поверхность с границейGelfand-Dickey hierarchyиерархия Гельфанда-Дикого
Publication based on the results of:
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