Open $r$-spin theory III: a prediction for higher genus
Abstract
In our previous two papers, we constructed an -spin theory in genus zero for Riemann surfaces with boundary and fully determined the corresponding intersection numbers, providing an analogue of Witten's -spin conjecture in genus zero in the open setting. In particular, we proved that the generating series of open -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 -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
Cite
@article{arxiv.2211.16302,
title = {Open $r$-spin theory III: a prediction for higher genus},
author = {Alexandr Buryak and Emily Clader and Ran J. Tessler},
journal= {arXiv preprint arXiv:2211.16302},
year = {2022}
}
Comments
The content of this paper was included in the content of the first versions (v1-v4) of arXiv:1809.02536, before we splitted it. It includes a discussion of the structure of open r-spin intersection numbers in higher genera. 13 pages